But that actually doesn't matter at all, because since the new Star Wars movie, they (the First Order, actually, but that's even worse for this scenario, since they're just a fraction of Empire, and thus have only a fraction of full Empire's capabilities) have a super-weapon (Starkiller) capable of destroying the entire Solar System from half a galaxy away. How many years it would take for Voyager to cross that insane distance, again? IIRC it was at least several dozen years. And Star Wars can just shoot down the entire Federation from that distance, like ducks on a range.
It would take less then a second for a federation ship to cross that distance at warp 4, i.e. a leisurely pace for even a runabout.
How do I know that it's a few seconds? Because that energy beam is travelling slower then the speed of light. We are shown people looking up from the surface of the planets in horror at the approaching beam. This would not be possible if it was FTL. So from this we can conclude that every one of those targets is in the same system.
...Either that or Star Wars jumped the shark and JJ Abrams gives zero shits about the lore or common sense.
Look sometimes in science fiction people fuck up and say things that make zero fucking sense. In Voyager there is an episode where they develop the ability to instantly travel across the galaxy and travel back in time while "evolving" into lizards... the less said about that episode the better. You dont hear me saying however that in Star Trek it's possible to do transwarp travel across the galaxy instantly on the basis of that episode. If I were to talk about transwarp, I'd talk about the reasonable stuff we see later. But honestly I'd rather not talk about transwarp at all.
So if you say that the Empire can blow up earth from the other side of the galaxy I will say that the Federation can travel back in time and make sure that Palpatine is put into a proper foster home. But in both cases you are relying on the worst thought out parts of the lore. I like the parts of the lore that are clearly established and come up a lot. Dont throw out the stuff that actually happens on camera on the basis of someones brain fart where they decided that the galaxy has eleventy septillion citizens or that lasers can travel between star systems.
How long did it take Voyager to travel halfway across the galaxy? Well it took them decades but there is a real discontinuity there. Federation ships regularly travel a quarter of the way across the galaxy in months. Yet it takes years to travel halfway across the galaxy. Surprisingly in all those seasons they never really explain why this is. My best explanation is that Voyager is facing some sort of constraint that keeps them from travelling like ships normally do. That is why it takes them two years to leave Kazon space despite the Kazon being so much slower then Voyager.
The republic was stable, and so was the empire for the majority of it's existence.
Dude, like one tenth of the old republic left to form the corporate sector IN ONE GO and they didn't even resist. This is on top of them completely losing track of worlds like Bespin, Tatooine or not even knowing about the existence of a sentient race on Endor. The empire has about as much control on it's territory as Afghanistan.