Diversity on Starfleet Ships

 If you watch pretty much any Star Trek show or movie, you'll notice that the vast majority of every Starfleet crew we see is human despite these ships representing a multi-species Federation. Why is that?

(I don't feel like doing a lot of research for this, so I'm mostly going to rely on my memory.)

Of course, the real-world explanation is that it would cost a lot more money to get a ton of actors into alien makeup and prosthetics for every single episode (this is also why there are so many alien species that look exactly like humans, especially in TOS). In-universe, it's a bit trickier to explain. From what I recall, there have been two different canon explanations given: one is that Starfleet usually has single-species crews, another is that for whatever reason, humans are just more interested in joining Starfleet than other species. Of course, these two explanations don't have to be mutually exclusive.

The first suggestion of species segregation in Starfleet comes in TOS, "The Immunity Syndrome", in which the all-Vulcan crew of the USS Intrepid is killed offscreen. Another all-Vulcan crew is that of the USS T'Kumbra, seen in DS9's "Take Me Out to the Holosuite". The USS Hera had a mostly Vulcan crew, though it was captained by a human, Silva La Forge. There may be other mentions of single-species Starfleet crews that I'm not remembering.

I don't remember any specifics, but I believe that there are multiple instances of non-Federation members basically accusing Starfleet of being an instrument of human imperialism, which is interesting. There are also other Federation member species, such as the Vulcans, which have their own service branches separate from Starfleet, which could add to the suggestion that Starfleet is a mainly human organization. (And this is no longer canon, but in the first two seasons of TNG it seems like the writers decided that the Klingons were Federation members while still having their own military.)

Another thing to note is that Starfleet crews' diversity has increased as real-world time has gone by. In TOS, Spock was the only non-human seen on board the Enterprise. In the '80s and '90s, we started to see occasional non-human crewmembers as extras/co-stars/guest stars, while we go to three non-human Starfleet regulars in TNG (Worf, Troi, and Data), two in DS9 (Dax and Worf [and eventually Nog as a recurring character]), and five in Voyager (Torres, Tuvok, Neelix, Kes, and the Doctor [though it should be noted his appearance is taken from a human] [also I guess you could question Neelix's and Kes's status as members of Starfleet]). The new shows now have much more diversity of species on their ships, a result of higher budgets than Star Trek has ever enjoyed before as well as perhaps a stronger desire on the creators' part to showcase the Federation's diversity. This has created a situation in which the Enterprise apparently had a lot more non-human crewmembers in the 2250s and early 2260s than it did in the late 2260s, which is a little weird, but oh well. You could maybe say that Kirk's Enterprise actually does have more non-human crewmembers that we just never see onscreen.

It does make sense that Starfleet might try to keep species separated. Different species might have different atmospheric, gravitational, and sleep cycle needs that would make it difficult for them to live in the same space. This is particularly explored in the DS9 episode "Melora", and in other episodes we see that Benzites and Barzans have to wear special apparatuses in order to breathe in environments tailored to humans. On the other hand, part of Starfleet's mission is to foster understanding between different species and cultures, and having diverse crews seems like a good way to help accomplish that.