I would love this.One trope that would require some serious rework of how the game begins: start in a decadent, stagnant and fully explored/colonized galaxy that is on the verge of galaxywide collapse -> old federations are about to break, the GC is unable to pass even the smallest motion, technology has to be rediscovered, new upstart empires are eating the old and declining, the central power/custodian/emperor is too weak to intervene... something akin the Old Republic, but with a heavy dystopian touch.
But that would outright cut the whole exploration and shift the focus on year-long diplomacy and politics. I'm not sure we have the level of refined mechanics we would need for this to be fun and engaging. (Well, tbh, I am sure we don't have that level - yet, I hope)
It seems very doable, too -- you'd need some mechanics which allow an empire to decline, or to fragment, and those seem doable.
Declining empires would eventually become Fallen Empires, static and secure but never expanding and seldom interacting with the wider universe. They'd lose all their worlds except a few core colonies.
Fragmented empires could shatter into mutually-antagonistic rivals which tried to destroy each other, and might succeed often enough to leave a "clean slate" for the next generation, or at least reduce their overall production capability and thus set back all fragments by decades of progress.
Then you could start "in the middle" of galactic history, and deal with empires in decline when you're starting, and then deal with vigorous newcomers when you're established.