As someone already mentioned, the Federation Council has very few human faces at all. I'll also add that the Federation president was often non-human, and that the Federation includes multiple non-human species who are visually indistinguishable from humans, so we actually don't really know how big the percentage of humans in Starfleet is, though they do seem to be the biggest group there. But there are also other important Federation organizations that we know very little about, so those could easily be dominated by some other species.
The Klingons are perfectly willing to cooperate with locals rather than conquer, given the right circumstances. We saw them winning hearts and minds on TOS multiple times, often by granting local people the technology to smite their enemies in exchange for local resources/use of their planet as a base.