Basically my ideal is an empty galaxy should be a political experience of managing an expanding empire that is otherwise trying to tear itself apart. And in a populated galaxy it'd be an extra challenge or aspect to going wide that needs attention that Tall doesn't need to deal with.
This is what I'd like to see too. I understand it's not the game everyone wants and it adds a level of tedium and frustration, particularly for people who don't want it, but I'd like for a 4X game to support interesting play if you are the only empire in the galaxy.
I've thought about it a fair bit while trying to build my own space 4X and I came to the conclusion that this is pretty tough to pull off in a meaningful, satisfying and not extremely frustrating manner. It's similar to the problems Dwarf Fortress has in adventure mode when Toady added the new emotional states: at some point you have to decide what the player is in control of and what they aren't, and it's not always clear cut where this should begin and end.
An example of that in an internal politics rewrite would be leaders who have their own agendas. It's realistic to have a governor aspire to lead a rebellion and leave your empire, and even interesting. But it's
annoying, especially if you have other problems in your empire to deal with.
A more direct example might be if the empire's leader had a personality separate from the player's. That starts to break down the meaning of who you are as the player and what you're doing, even if it's again realistic and could help to bring things like dictatorships more into line with reality where sometimes you get an idiot who inherits the throne for 100 years and derails an empire. Or you elect an idiot in a democracy who ruins it for their political term. It's realistic but nobody is going to want to deal with that as a player.
Simply turning sectors into pseudo vassals with no special core sector is probably what I'd vote for. They could have different levels of contribution to the empire, could potential revolt, and may have political conflict over ethics even. It would be interesting if sectors could be treated as mini empires like vassals in that regard, where ethics drift was a thing you had to actually manage.