I'm sure the practical reason behind having a nearly all-human crew in TOS is obvious, so I'm not going to go down that road.
I can't remember which episode it was, but there was one where they encountered another Starship that was manned entirely by Vulcans. Seeing as how the Enterprise was almost entirely manned by humans, and how McCoy still wasn't able to understand Spock's physiology that well, I think it makes sense to assume that this was the common practice in the TOS era. It makes sense, because you hardly ever see anyone from the founding member planets of the Federation unless they have a cause to deal with them. It probably reflected a different mindset when it came to leadership and maybe even mission tasking - Andorian crews would be best for simple combat missions, Vulcans for diplomatic or scientific missions, and Human crews for things like the 5 year mission (where they didn't know what to expect).
Obviously by TMP's time they had begun experimenting with a new command philosophy, and by the time of Enterprise D, they wanted to have a wide variety of peoples to carry the flag of the Federation.
I can't remember which episode it was, but there was one where they encountered another Starship that was manned entirely by Vulcans. Seeing as how the Enterprise was almost entirely manned by humans, and how McCoy still wasn't able to understand Spock's physiology that well, I think it makes sense to assume that this was the common practice in the TOS era. It makes sense, because you hardly ever see anyone from the founding member planets of the Federation unless they have a cause to deal with them. It probably reflected a different mindset when it came to leadership and maybe even mission tasking - Andorian crews would be best for simple combat missions, Vulcans for diplomatic or scientific missions, and Human crews for things like the 5 year mission (where they didn't know what to expect).
Obviously by TMP's time they had begun experimenting with a new command philosophy, and by the time of Enterprise D, they wanted to have a wide variety of peoples to carry the flag of the Federation.