The Soul King is the linchpin of the worlds of Bleach, and it was created with the purpose of stabilizing the flow of souls into and out of Soul Society, which had previously been rendered "unstable" by the flow of soul. The fact that a Soul Society existed before the Soul King was created indicates that the worlds could indeed exist without the Soul King as their linchpin. Because of his current existence as the linchpin, killing him is said to cause all the worlds to vanish into oblivion.
But is that truly the case, since the Soul Society and Living World existed before the Soul King? Is this collapse a consequence of what the Soul King does to "stabilize the flow of souls"; did the Soul King's power as the linchpin change the fundamental existence of the worlds into ones that cannot exist without him?
Why can Quincy blood not forgive the existence of the Soul King? Is there more to the Soul King's power than to stabilize the flow of souls?
While the subject of the Quincy's survival has given me a sore spot as of late, there are certain factors that have failed to add up ever since Bazz-B and Haschwalth's back-story was revealed. Yhwach calls himself and is believed to be "the father of the Quincy" by his followers and those who hear the stories about him. But in Bazz-B's backstory, he talks about a Quincy folktale regarding a rare occurrence of Quincy born incapable of gathering reishi. Those Quincy were culled when young as aberrations, and the last one born like that before Haschwalth was two hundred years prior, whereas before such Quincy were born every few decades. As we saw in the backstory, Yhwach was that Quincy, born with the ability "to share power with others", just like Haschwalth.
What is important to take from this is not only the existence of unique Quincy (odds are Ginjo and Ichigo might be such Quincy), but the fact that this folktale spoke of Quincy pre-dating Yhwach. If Quincy pre-dated Yhwach, then he could not truly be the "Father of the Quincy", regardless of what was said about him even back then. Moreover, Yhwach is the son of the Soul King, and Pernida said, in a manner reminiscent of royalty, "I have always been a Quincy". Since the Soul King is Yhwach's father, that verifies the existence of Quincy before Yhwach, in a manner of speaking.
Which brings up the question as to when rumour or fiction became reality. When did Yhwach truly become the "Father of the Quincy", whose blood flows in the veins of all Quincy?
I believe it happened in the Quincy-Shinigami War a thousand years ago, and the creation of the Soul King.
Yhwach, when he killed Yamamoto, talked about how the original Gotei 13 exterminated the Quincy, and said "the Gotei 13 died with us a thousand years ago", referring to the Quincy whom Yamamoto exterminated. Despite this, the Quincy still exist in the modern day, and all of them have Yhwach's blood flowing through their veins. To be more specific, all Quincy bear a piece of Yhwach's soul.
So how is that no Quincy have been born outside of those who bear a piece of Yhwach's soul, when Bazz-B's backstory implies that was not always the case?
I believe it all goes back to the entity the blood of the Quincy cannot forgive - the Soul King. If the Soul King is responsible for "stabilizing the flow of souls" into and out of Soul Society, it is entirely possible the Soul King's power even extends to influence the "nature" of souls as they go through the "flow of souls", or even decide where souls go when they die.
In other words, the Soul King could have been preventing any new Quincy being born in the Living World, and may even be the reason why it is believed a Quincy's arrows "erase Hollows from existence".
The idea that the Soul King is preventing new Quincy from being born, outside of the bloodlines which already exist, goes back to the idea of the "memories of reiatsu". The reason why Ichigo's Quincy power came to the surface was a result of Quilge's reiatsu being drawn into his soul after pushing himself to his limits to escape "The Jail". This means that Ichigo's "racial ability" as a Quincy was a "memory" that was dormant until awakened.
What if the Soul King does something opposite of that on a grand scale - whenever a Quincy soul dies and is eventually reborn in the Living World, the Soul King's power to "regulate the flow of souls" allows him to "bury" the soul's memory of their Quincy potential, causing them to reincarnate as normal Humans.
This may be why Quincy have only been born in the past thousand years to Quincy who bear a piece of Yhwach's soul - the piece of Yhwach's soul keeps the "memories of the Quincy" alive within the bloodline, perhaps as one of the "miracles" said to occur as a result of being given a piece of his soul. But this only works so long as the bloodline is "pure", because we know that inter-marrying with Humans may "weaken" Quincy potential.
I am by no means trying to justify the entire Gemischt and Echt Quincy separation; I am trying to explain why it might exist at all in the context of this theory. According to Isshin, an Echt Quincy naturally possesses the ability of Blut, whereas a Gemischt Quincy has to train in order to acquire the ability. It is possible that the influence of Yhwach's soul was weakened when a Quincy has a child with a Human, and as a result the Gemischt child's "memory" of the ability Blut was buried.
Suppose that, if a Gemischt child then married a Human, their Quincy abilities could either weaken further or vanish in their entirety, leaving the child born between a Gemischt and a Human a pure Human, the "Quincy memories" of their soul completely buried.
Given the Soul King was created by the Shinigami, it is likely the Shinigami wanted to erase the Quincy from history forever, since we already know that they have been erasing the Quincy from even their history books and the Academy's curriculum. As to why they would do this, the likely answer would be that the Quincy a thousand years ago posed some kind of threat to the Shinigami's authority. One could say that this is due to the Quincy's arrows "destroying" Hollow souls, because Quincy advocate the through killing of Hollows rather than sending Hollows to Soul Society.
Yhwach's existence gave another possibility to the final destination of Hollow souls - being killed by a Quincy arrow causes the soul to be absorbed by Yhwach, explaining why the Shinigami do not know where those souls go.
But this theory advocates another possibility: Hollows killed by a Quincy could reincarnate as new souls in the Soul Society (the initial description indicates only the piece of Yhwach's soul goes back to him, not the entire soul), but the Soul King prevents that.
NOTE: The other option is that Hollows originally killed by Quincy went to Hell, because they do not "purify" Hollows of their sins, so Hollows are sent to Hell for their sins committed as Hollows. That is what I believe happens when any Hollow is killed by any means other than a Zanpakuto (yes, even Fullbring).
The Soul King "regulates the flow of souls" into and out of Soul Society. This indicates a strong influence over souls as a whole, Human and Hollow alike. How a Shinigami Zanpakuto "purifies" a Hollow soul has not been explained in detail (we know "what" it does, but not "how" it does it), while we are told that Quincy arrows "destroy" Hollow souls. Perhaps it is not that a Quincy arrow "destroys" Hollow souls, but that the Soul King's power keeps those Hollow souls killed by Quincy from reaching their destination.
If that is the case, where would the Hollow souls go? I can imagine two possibilities right now:
1) they fall into the Garganta and vanish entirely, unable to go to Soul Society because they are not "regulated" to Soul Society by the Soul King.
2) They fall into the Garganta and become Kyogoku.
There is a third possibility, but I will get to that later.
What Yoruichi said about the Kyogoku is that they are composed of "stray souls", and that Soul Society does not know how they remain stable in the Garganta outside of having a unique reishi composition compared to normal reishi.
This is very suspect, because the Soul King's ability to "regulate souls into and out of Soul Society" should mean that "stray souls" should not escape just like that, and in a large enough quantity to form a number of pocket dimensions ranging from small to large, no less. One could claim that these build up over the course of a thousand years at minimum, but this might not be the case.
The Valley of Screams could be dimensions that formed from the gathering of Hollow souls that were killed by Quincy, but were stranded in the Garganta because the Soul King's ability kept them from entering the Soul Society. This would create the 'illusion' of Quincy destroying Hollow souls completely, as it is possible these souls became untraceable when lost in the Garganta, giving the Shinigami that impression. This congregation of souls could explains their unique reishi structure, as they would be dimensions of Reishi created from Hollow souls.
Now, moving on to the final aspect of the Soul King's power - his status as the linchpin. The Soul King "regulates the flow of souls", and his death, as demonstrated, led to Hueco Mundo, Soul Society and the Living World experiencing earthquakes as they started to collapse. Soul Society was most heavily affected, as the world literally began to come apart, whereas the Living World only experienced perpetual, minor earthquakes that only the spiritually aware seemed to be aware of. So there is truth to the Soul King's existence as the linchpin of reality.
But how did that truth come about?
Before the Soul King existed, souls naturally flowed into and out of the Soul Society. The implication is that they did not need Shinigami to send souls to Soul Society via Soul Burial (discounting those who were bound to the Living World by their desires), and that souls might have been able to make it to Soul Society on their own. There are many stories of living Humans travelling to the Afterlife in various mythologies and religions, and coming back from the Afterlife. Perhaps, in the distant past, this was true in the Bleach universe, and the Jureichi may have once been a hotspot for such pathways to the Soul Society.
NOTE: I say the above because it would explain why the piece of land where the Jureichi is specifically is required to create an Ouken.
In other words, Soul Society, the Living World, Hueco Mundo, Hell and even the Dangai were all different dimensions existing in the same space without touching one another, just as the Vandenreich existed in the shadows of the Seireitei. Because they existed in the same space as one another, pathways between the worlds naturally existed. In the case of the Soul Society, this connection between Soul Society and the Human World accounts for the vast and chaotic flow of souls into and out of Soul Society that made it "unstable".
When the Soul King was created by the Shinigami, the Soul King separated the dimension from one another. Hueco Mundo was cast off from the other dimensions; the Dangai was turned into a bridge between the now-separate Soul Society and the Living World. I can only assume that Hell and the Living World, for whatever reason, are still directly overlapping one another, as we saw no Dangai or Garganta or anything similar separating the Living World from the domain of Hell when the Doors of Hell first opened in chapter 12.
Urahara stated that, when the distortions caused by Quincy killing Hollows appear and disappear, a massive amount of energy, enough to connect Soul Society and the Living World, is released. We have been told numerous times that the Soul Society will collapse into the Living World because Hollow souls killed by Quincy do not return to the Soul Society, causing the number of souls to only increase in the Living World, and that this collapse will result in the destruction of both worlds. What if this "collapse" is not the product of the worlds veering towards their mutual destruction, but a product of the worlds returning to what they once were?
Although the Soul King initially separated the worlds, the "balance of souls" is all that is keeping the Soul Society and the Living World separate from one another, and keeping them from returning to their natural state - as overlapping dimensions existing in the same space. However, the Shinigami painted it as the Quincy's actions leading towards the destruction of the worlds in order to give them the justification required to massacre the Quincy once more, leading up to the Quincy Massacre of 200 years ago.
A thousand years ago, the Shinigami asserted their dominance over the system of souls by exterminating the Quincy, leaving only those who followed Yhwach and his Quincy into the Soul Society and the Vandenreich as the sole survivors; two hundred years ago - synchronous with the birth of a new Quincy with the ability "to share power with others" - the Quincy who repopulated the Living World became too numerous and too much of a threat, so another Massacre was carried out under the pretense of saving the world from destruction.
In other words, I believe these are the purposes which the Shinigami created the Soul King for:
1) To regulate the flow of souls into and out of Soul Society
2) To keep new Quincy souls from being born in the Living World (outside of those who bear a piece of Yhwach's soul)
3) To prevent Hollow souls killed by Quincy from reaching their destination, giving the illusion that they destroy souls.
The separation of the worlds from one another is an extension of the Soul King's power "to regulate souls" - keep Human souls from reaching Soul Society on their own and make them dependent upon the Shinigami. The distortions and the imbalance caused by Quincy destroying souls are a result of the "flow of souls", which is necessary to keep the worlds separated, being disrupted, thus causing the possibility of Soul Society and the Living World returning to being worlds that exist in the same space as one another.
The third purpose might seem counter-productive given the consequences, but it is productive in the sense that it gives Shinigami motive and reason for wanting to discriminate against, limit the number of, and kill Quincy. If the Quincy's actions are painted as being dangerous to the existence of the world, that is all the Shinigami need to exert their authority and to wipe them out "for the sake of preserving the worlds".
This all depends on what the truth turns out to be in the future. Now that Yhwach is the new Soul King, we may see what that entails, depending on what he uses the power of the Soul King to accomplish (or undo).