It's too easy to make world-busters for a long terme, sustained conflict to be viable. If war is constant, it's doctored. If peace happened, the various governing bodies would probably have to relinquish emergency war powers and be held more accountable. So, let's have an hereditary enemy who could planet-bust your populations centers.... but for some reason, mainly because it would make your own people consider using them, doesn't. Instead, there is a lot of skirmishes around the contested zone (of absolutely no strategic import since there is hyperdrive) so you can show the populace 2D maps of the galaxy showing a dubious border in blue and red, explaining why there is a need to be ever vigilant.
People would probably notice and speak up, but everyone knows what happens to unpatriotic people during war time: the cinema industry is regularly under scrutiny in all of these empires. Having dozens of empires allows for various opponents and threats. Most citizens of these empire would never be confronted with the war, but keeping it a looming prospect is a must.