Depending on how sectors are built up (lots of starbases/fortresses, or labs/unity buildings, or food/civilian industries), your economy could influence ethics attraction, leading to some sectors having a good amount of its population materialist, or militarist, with different policy desires. Also, what are your thoughts for sector events that could occur throughout the game, with impacts and effects on your culture and politics? Maybe a planet wishes to be apart of a different sector, or a sector which is right up against another Empire starts shifting to their ethics, and wishes to trade (if they're neutral or better)?
Sector edicts could be cool, and could cost unity, as a sink for it. So you can trade progress on Traditions for a decent edict in your sectors. Maybe you're in a war, and you have a sector which holds several shipyards, so you enact an edict which buffs build speed and decreases ship cost. This makes the militarist pops happy. Could there be sector policies as well? Basically, what we have now in many policies, on a sector instead of Empire level?
Handing off patrol fleets would be nice to decrease micro, and if you're a trade heavy Empire, it could get to the point that the sector becomes powerful, and wants to secede to become a vassal or ally instead.
I like the idea of sectors cooperating. Maybe this could be apart of the "Interstellar Incorporated" mod which uses freight ships to transport resources.