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.