Sorry, I'm not seeing a problem here.
As said earlier, Star Wars is an elaborate fairy tale. Once the evil space wizard is defeated, poof, that's it, it's over. Good guys win and live happily ever after....
If you want an "in universe" answer, well, it's directly stated in ANH that the Emperor dissolved all of the political bureaucracy (the Senate). The Emperor controlled everything. There was no other political institution to link all the systems. And The Emperor wouldn't be able to maintain control of all the systems without fear. Fear kept the the galaxy in line, certainly not loyalty. Once the Death Star II was lost, the Emperor defeated, the Empire embarrassed by ewoks -- and no more galactic senate to provide central organization -- it's not hard to imagine that each system was now on it's own. No more Emperor to answer to. No consequences for acting unilaterally. Essentially, each system would be no different than if it were in the outer rim. Maybe there was a small Imperial garrison to deal with on each system. But as we saw in the SE clips, strom troopers were literally being over thrown, so I doubt it was a big deal. And maybe some of the Imperial fleet remained...but so what? There was no centralized rule. There was no political power to back it up. What are they going to do? Re-conquer every system one-by-one? The Empire was smoke and mirrors. The only thing keeping it together was fear. By the end of RotJ, that was no longer a problem...