I think part of the issue is how relatively rarely we are shown other star-faring democratic societies in the Franchise in general, or ones comprised of several species in particular.
If you look at the Star Fleet Universe, the UFP in that setting is in the same neck of the galactic woods
as at least two other democratic powers; the Gorn Confederation and the Inter-Stellar Concordium (both of which should be familiar to anyone who played the first two Starfleet Command
Of those, the ISC
in particular is notable in also being a major power comprised of several member species; one which took a very different path to integration than the Feds did, but which helped shape the quite different political outlook it had in the modern era of the SFU.
There are other (at least partially-)democratic societies in other parts of the wider setting, such as the Męsron Alliance over in the Omega Octant.
Plus, the UFP itself in that setting is noted to have a number of independent worlds within its trusteeship territory, but which retain their independence from the Federation (even when, in some cases, the worlds in question would easily qualify for membership, and whose governments are on good terms with the Feds).
In contrast, it's hard to stop and think of which other powers in the Franchise have such democratic credentials; the Alpha and Beta Quadrants are filled with less open (to others) societies, the known Gamma Quadrant is dominated by the Dominion, while the smattering of Delta Quadrant powers we are shown on-screen make for somewhat slim pickings (which may be part of the point; perhaps the Borg had already made a point of knocking off any would-be planetary unions in its rise to power, forcing the rest of the quadrant to try and make as little political noise as possible).
Even in the case of the Xindi, we only see them through the lens of the conflict with Earth and the manipulations of the Sphere Builders; perhaps they make a better go of being a stable multi-species union during peacetime? (Assuming they don't end up as yet another bunch of Federation members by the time the -J is in service, that is).
One day, it would indeed be interesting if the Franchise was able to take a look at a compelling counterpart to the Federation, in the sense of there being another multi-species democracy out there that would have its own set of ideas as to how to go about their business; but finding the right place for such a story to be told would be the real trick.