Cyclops is definitely more comfortable with field leadership than political intrigue.
Separation of political and military structures
I also don't think Cyclops NEEDS to be on the council, story-wise, but I just want to give a reminder that Cyclops already ran a mutant nation with Utopia, and did it damn well. It may not have been to the scale of, or as recognized as Krakoa, but he was so good at it Namor and Mags both bent the knee. He IS actually experienced with and good at dealing with politics, playing the media, and spinning mutant public relations. The best reason to leave Cyclops off, as I see it, is that Hickman sees more interesting drama in the future with Cyclops answering to higher powers, including villains, not because it's not his field. He would actually be the best at it.
Edit: An in-universe possibility is that a new nation doesn't need the baggage from the last 6 years of Marvel writing Cyclops to be a volatile weirdo that makes wolverine seem to be the sensible role-model by comparison. You know, The Lost Decade.
About universal societies: PoX#2 was good about defining the relationship between Technarchs and Phalanx and then retconned the Phalanx we were previously familiar with to be merely a Technarch. But PoX#5 seems a little sketchy on the Phalanx's relationship with the higher societies. It made sense that Phalanx used Technarchs because there was a clear purpose, but it's weird that they now suggest Phalanx are also used by Titans, as if it's only a given that higher societies daisy chain into lower societies. I don't see why that necessarily has to be the case. Are Titans intelligences confined to their singularities and can no longer interact with normal space-time and are forced to employ more primitive societies to carry out their will?