24th century uniforms should be able to accommodate biology and enviroment, if Vulcans can make babies with humans they can suck it up and work with them on a starship for a few years.Aliens from even close-to-Earth-like environment may be uncomfortable for day-in and day-out living. For example: Vulcans. Earth ships are too cold and stink, plus you are around annoying people from another culture. Humans probably feel the same on a Tellarite or Andorian ship. It's just not a policy decision but a biological reality. You may find one or two exceptions who are willing or tasked with a foreign assignment but they may also need medical treatments and special clothes.
A human dominated starship as the Federation flagship makes as much sense as having the Enterprise NX01 representing a United Earth spacefleet dominated by white Canadians...
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