My suspicion is that this is a combination of institutional inertia growing out of the founding worlds' original fleets, and of issues with biological compatibility and potential cultural conflicts.
So we might have seen the early Federation Starfleet practice de facto species segregation essentially by allowing the crews of Vulcan, Andorian, Tellarite, and Human ships to continue serving amongst themselves when it folded the Vulcan, Andorian, Tellarite, and Human space services under the Federation Starfleet banner. This may have been both a concession to prejudice and the history of inter-species conflicts, and to more legitimate concerns about how to integrate space services with vastly different operational cultures.
Over time, I imagine that Starfleet has gotten better at inter-species integration, with segregated ships or mostly segregated ships being less common. This seems to agree with the canon, which has gradually increased its depictions of non-Humans aboard Starfleet ships and stations. So maybe by the 23rd Century, we'd see a mostly-Human-with-a-Vulcan ship like the U.S.S. Enterprise
NCC-1701 (or maybe a mostly-Andorian-with-a-single-Tellarite ship like the U.S.S. Kumari
NCC-1702, or a mostly-Vulcan-with-a-single-Andorian ship like the U.S.S. ShiKahr
NCC-1703); and then by the 24th Century, we see a ship with a Human plurality but a significant multi-species minority like the Enterprise
-D (with corresponding other pluralities on other ships); and perhaps by the 25th Century, the Enterprise
-H is so thoroughly integrated that there's no real species dominance in its crew makeup.
The novels have addressed the question of inter-species integration in the Federation Starfleet. Part of the premise behind the Star Trek: Titan
series is that the U.S.S. Titan
, and its other Luna
-class sister ships, was explicitly designed to have the most biologically and culturally diverse crews ever seen.