I mean the official rank and position of captain. In the reboot, Spock was only acting captain after Pike got nabbed, IIRC.

Well, on the show that's mostly a budget issue. They have to pay to put funny foreheads/skin-paint/neck-pieces onto the aliens, ya know. After the main cast and the alien of the week, they really don't have enough money left over for the one-shot other Starfleet ships/personnel that occasionally show up. In the expanded canon (comics, later "official" books, etc.) there are more non-human captains and crew in SF.