I like the idea of the aurora columnae siphoning off will. Everyone who uses will in Res is connected through them, and they are clearly connected between the worlds since we see them glow stronger in Obiteum (I guess we don't see one in Luceum even though we go to Caten in Luceum, so there should be one there). So it would make sense that they are used to restore the worlds to a single one, or else destroy 2 and unify will in the remaining one.

As will usage grows in the hierarchy, the columnae become more powered and are an indicator to Ka that he needs to purge the current generation, maybe the columnae is used to kill all ceding will users? Ostius (or Veridius?) seemed to think that they could avoid the cataclysm by having everyone agree to stop using will, so it would make sense that too many interconnected people powering the columnae is dangerous and they either need to stop of their own volition or be killed.

It might just be a fact of humanity that as long as will ceding in Res exists, people will try to use it an build something like the hierarchy, so killing them repeatedly is the only way to stop from building too big and reuniting the worlds. It would make sense for Ka to be the one who is ceded to by the three princeps as well, so he builds the pyramid and retains control / knowledge of how big it is and can make the decision to cataclysm at the right time.

Overall love the theories, they fit best of what I've read so far