Cultural imperialism, the defining motto of Starfleet. All personnel must use standard human ranks, ships, uniforms and methods of relaxation.
I do believe that the races within UFP do maintain their ships, even though we never actually see them. I remember being mentioned in a DS9 episode about a planet charted by a vulcan ship.
And there are also those episodes in TNG taking place in Romulan space that involve vulcan ships.
As we never actually meet most of the races in UFP except for some temporary characters, there's no way of knowing their ships.
For that matter, it's rare enough just to encounter other Stafleet vessels, and the only times we DO is when some Starfleet VIPs are coming aboard the Enterprise or when something really scary is happening relatively close to Earth (and I think by now it's a foregone conclusion that both the Klingon and Romulan empires are both much closer to Earth than they are to most other Federation members).
The large fleets of DS9 seem to suggest we are "finally" seeing what all of Starfleet looks like, but in context that's unlikely. MOST of those ships are a hundred years old and probably fresh out of mothballs; I wouldn't be surprised if the Hathaway
wound up getting pushed back into service to fight the Dominion (or Stargazer, for that matter). That, therefore, would be Earth's Starfleet making its contribution on their specific front of the Dominion War. It stands to reason the Suliban and the Xindi probably had a pretty rough time in the Delphic front as well.