Basically, the need to ask might never emerge, either. One day, people would just wake up to such a significant number of cultures having joined the Federation that the rest would have to join, too, or else be declared the enemy and crushed, for being so perversely deviant.
Or simply for being incapable of sustaining a separatist lifestyle, what with being surrounded at all sides. The "crushing" could take all sorts of soft forms and involve no weapons fire or even any harsh words. But it's also possible that the UFP would unite against a common foe after common foe, growing bigger and more unified at each step, until becoming incapable of dealing with opposition or difference except through the force of arms.
With classic warp drive, the galactic empire could not be conventionally governed, as it would take decades to access the farther parts. Quicker means of travel are fairly easily available, though, and were there pre-Burn in the galaxy-spanning Federation we witnessed; perhaps those might be expensive things reserved for the needs of the central government, but still.
Yet a culture that is in the process of expanding through the galaxy would probably go unstoppably galactic even with sublight travel, much like the Greek remained Greek despite scattering across the Med. The resulting galaxy might be a pulsating mass of locally emerging new ideas, always stretching this way or that, but never quite breaking off into empirelets, exactly because the new ideas would travel relatively slowly and would always be washing over each and every location more or less evenly. Until something gave.
We know the Slavers went down, but we don't know if the specifics match Larry Niven's Known Space backstory. We can also assume the proto-humanoids eventually ceased to be, but whether through ascension, fragmentation, replacement by their deliberately created offspring, or perhaps some natural disaster or collapse, we have no idea. The Federation collapsed on dilithium shortage, but might rebound after a mere century of chaos. The Dominion has been stable for ten millennia if their propaganda is to be believed. So it might well be that it's the destiny of driven star empires to go galactic, and then stay galactic, until something truly exceptional happens, perhaps only after millions of years of prosperity and stability.
Timo Saloniemi