Concerning why the Federation is so UE dominated and why the resulting military was more an evolution of Earth's own military more than anyone else's...I had my more diabolical idea over that. I began to think that Earth deliberately held back in the Romulan War and allowed it's allies to be devestated in the conflict (greatly weakening the Romulans as well) and only stepped in when both the allies and Romulans had pretty much wasted each other. Earth made the agreement that in exchange for them defeating the Romulans it would be Earth as the dominant power of the new alliance that would have to be formed from the remains of the allies power (since alone too much of their individual infrastructure had been destroyed and they'd have to work together more closely). Then after they beat the Romulans Earth essentially whitewashed the history books to make it the "Earth-Romulan War" and downplayed the allies' involvement.
So from this, the TOS Federation was really a benevolent Terran Empire with the other aliens as weak partners.
It's certainly an interesting proposition, but I find myself doubting that it's likely for a couple of reasons.
When we last left the canonical 22nd Century, United Earth had already damaged three major Romulan operations in local space. It was Humans who helped Vulcans overthrow the Romulans' puppet government on Vulcan with the coup against Administrator V'Las and the dissolution of the High Command. And it was Humans who stopped the Vulcan invasion of the Andorian Empire. And it was Humans who thwarted the Romulans' attempt to provoke war between Andor and Tellar.
As a result, right off the bat, it seems likely to me that the Romulans have it out for Earth. They're not as likely to target Vulcan, Andor, or Tellar, because all three of those worlds have proven vulnerable to Romulan manipulation, and Earth has thwarted all three attempts to control them. To the Romulan mind, Earth already constitutes the biggest threat to their interests -- making it unlikely that the Romulans would start gunning for anyone other than Earth.
There's a piece of canonical evidence about the Earth-Romulan War that might undermine your idea. In "Homefront," Sisko claims that a Jem'Hadar invasion of Earth will be the sort of conflict Earth hasn't seen since the Founding of the Federation -- implying that the Earth-Romulan War reached, and badly damaged, Earth itself.
On top of that, I don't think the Federation itself is particularly United Earth-dominated. Of the four Federation Presidents we've encountered, spread out over two hundred years of Federation history, only two of them have been Human -- Jonathan Archer twenty years after the Federation was founded (if you accept the bio screen in "In A Mirror, Darkly," at any rate), and the unnamed Human (named Hiram Roth in the novels) in 2285 (Star Trek IV). Meanwhile, we've seen two aliens as President -- an Efrosian in 2293 (named Ra-ghoratreii in the novels), and a Grazerite in 2372.
When we saw what appeared to be the Federation Council in ST4, it didn't seem particularly Human-dominated. And the guy who was apparently the most powerful foreign policy advisor to Ra-ghoratreii was Sarek of Vulcan. To top it all off, we never encountered the United Earth ambassador to the Babel Conference in "Journey to Babel" as we did the Vulcan, Andorian, Tellarite, and other ambassadors.
So I would argue that even if Starfleet is Human-dominated -- which I don't know if I agree that it is -- the Federation itself probably is not.