I feel like they should make sectors both more autonomous, yet also offer a bit more control. I'd love to have governors decoupled from the leader pool; The player can't generate a governor but every planet and sector has a toned-down CK2-style leader, with a couple traits based on their planet/sector focus, who contends with other governors and the player (asking for one system or another to be put under their control, planet governors asking to be made into a sector, vying with each other and the player for minerals/energy, trying to get more autonomy or even forcing a demand upon you to allow them independence or see civil war (with an auto-generated fleet based on your fleet power and the sectors income, with the in-universe justification that they've been syphoning off minerals to create a secret fleet))
Expanding on that, I'd like each sector to be a faction in my empire, lead by the governor, who need to be appeased the same as a faction (though with different bonuses, like getting more minerals out of them or energy/research, or preventing civil war and governors colluding to a la a CK2 independence faction) and with ethics based on the dominant ethics of that portion of your empire (and those ethics being the governing ethics of the new empire if they do become independent) I'm not sure that each planet should be a faction though... That would quickly fill up the faction list.
It always felt weird to have half my empire leaderless because I have 3 or 4 science vessels (which is a small number even then) 2 fleets and an army, plus the 3 reserachers. That only leaves you with 1 or even 0 governors from the beginning, and only a small number within a decade or two.
Obviously this idea is most suited to democracies, and least suited to dictatorships, but it can probably be molded a tad or just be a Democracy-only system (seems a lot of work to just use for one government type, at least without some corresponding systems for the others, though hell, even Hive Minds can use it, if they're of the Zerg/Bugger variety where there are multiple Queens/Cerebrates each controlling a portion of the species and sometimes fighting or vying with each other)
As for the bit more control, I was just thinking of like, allowing the expenditure of influene to force a building to be built on a slot. I.E. if you really want them to build that clone vats, or the mineral/energy production multiplier building, or when the AI simply refuses to upgrade that spaceport or the planetary HQ, etc.