The human dominance of the Federation does seem unrealistic at first blush. On the other hand, if someone wrote a science-fictional series in the nineteenth century and that series depicted Americans (Yankees, USA-ers) dominating the global politics and alliances of the mid-twentieth to early-twenty-first centuries, I'll bet readers would raise similar objections: "If there was a real-life NATO or United Nations, I doubt people would allow new-kids-on-the-block Yankees to dominate so much of it. Why should they?" Yet here we are.
And the comparison is not merely analogous. The Starfleet and Federation of the original Star Trek were largely modeled on and allegorical of post-WWII USA and its constellation of global allies. In other words, right at the time the USA took a huge step forward in global dominance, a US television show aired about humans who'd recently taken a huge step forward in galactic dominance.
What Star Trek never provided, to the best of my knowledge, was an analogous explanation for the huge step. There's no allegorical event equivalent to WWII (I suppose we could consider the Romulan War) and no allegorical technology equivalent to atomic and nuclear weapons. Instead of providing such explanation, the Generation-era spin offs (aired in a later, arguably less history conscious America) strayed from the original premise. The UFP is no longer a science-fictional USA, at least not so obviously. But because of the limits of production and audience expectation to which you allude, the UFP remains dominated by humans and in fact dominated more or less by Americans with the typical Hollywood look, which is less defensible with the original premise abandoned.