Vulcans were the first alien species to contact Humans, but after Enterprise, they have not been shown in higher positions among the Federation or in serials other than Commander Tuvok (as far as I remember).
Is the Vulcan story arc so boring or unappealing that the first contact species was discarded?
The only reference I can remember as to why they are not in many war situations is that they are pacifists as referenced by that Ferengi who is questioned by Commander Riker.
Out of universe, the reason why there are very few Vulcan stories in Star Trek TNG (and to a lesser extent DS9 and Voyager) is that Gene Roddenberry explicitly barred potential writers from writing stories about them:
"No stories about warfare with Klingons or Romulans, and no stories with Vulcans. We are determined not to copy ourselves and believe there must be other interesting aliens in a galaxy filled with billions of stars and planets" - Star Trek: The Next Generation Writer/Director's Guide
Ultimately, there was a conscious effort on the part of the studio to make shows that were at once similar to the old TOS show (notably the look and feel of the tech and the camaraderie of the crew) but also dramatically different (by introducing new aliens and situations).
It wasn't until after Roddenberry's death that a number of sacred cows seem to have been dispensed with, notably the prohibition on writing episodes based around the earlier crew and episodes containing Vulcans.
They are members of the Federation. Other species independent of the Federation with their own nations operate starships usually fully staffed with their own kind.
The Federation does not practice segregation, so all starfleet ships are fully integrated.
There are Vulcan captains, at least one: https://memory-alpha.fandom.com/wiki/Solok_(Captain)
The Vulcans have not colonized many worlds, and their society is a stable democracy. It is unlikely they will often require help from the Enterprise.
