One of the more contradictory aspects of “Star Trek” is the fact that although the United Federation of Planets is supposedly made-up of over 150 different and presumably equally represented races, when it comes to the presentation of those races in Starfleet it is quite normal for Starfleet crews to be often 80% human. Does this point to an inherent racism within the Federation, that it is in fact like the British Commonwealth, nominally an alliance of common nations but in reality dominated by a single member? The original series, probably due to sloppy writing more than anything else, tended to veer between the Federation basically being a human alliance, and occasionally accepting that humans only played a part in it. As with most things in a multilateral political union, the answer is probably multifaceted.
The real-universe answer is simply that it’s cheaper to have a bunch of actors who don’t require prosthetics and alien makeup. The original series pretty much gave up on there being too many aliens in Starfleet. Having said that, JJ Abrahams made a much greater effort in his three movies to show diversity in the Starfleet crew.
The first possibility is simply that there are other ships where the human contingent maybe very small or even non-existent. Some episodes of Star Trek have indeed shown all-Vulcan ships, and like NATO it would not be surprising, for coherence, to have some ships where a single race or culture dominates. A ship with a single race can have a single temperature or climate that suits the whole crew. Indeed, there have been episodes where Federation members (again with the Vulcans) have maintained ships separate from Starfleet entirely.
There’s also one other reason: maybe humans just like space travel more? As in the European Union, maybe every Federation member has a quota of Starfleet officers it’s entitled to fill, but most don’t, and humans are then permitted to fill the surplus places. It’s also possible that the other races are quite happy for humans to go off getting themselves killed on their behalf: after all, most of the Federation’s casualties fighting the Borg and the Dominion were almost certainly overwhelmingly human too.
Interestingly, the issue also raises the question as why Kirk’s original monologue, “…where no man has gone before” is actually more accurate and actually less racist than the (at the time) more politically savvy “…where no one has gone before.”
Why? Because “no man” is suggesting that this may be the first time humans are encountering some new sector of space, whereas “no one” suggests that the new races encountered are inferior to Federation species. Think I’m splitting hairs?
Ask yourself this: did Christopher Columbus go where no one had gone before, or just where no Italian had? I know what the Cherokee, Choctaw and Apache thought.