My theory is that the other members of the Federation saw humans as a bunch of chaotic, violent monkeys that somehow had gotten into space and in time would spread their flavor of chaos and violence across the universe.
So it makes sense they thought better training the puppy before it grows up.
My variation was that humans were the wildcard. Everyone else had long-standing tensions, but no one had a history with humans. There is that connection to the Vulcans, but Vulcans treat humans as children so it’s neither a friendship nor enmity
And the humans breed like crazy - at least, given what we see in the different ST shows; humans FAR outnumber the quantities of any other race. Even in the Undiscovered Country, one of the Klingons remarks that the Federation is little more than a "Humans only" club. So it was like, join them, train them, or we're going to be overwhelmed by them!
I think it's not quite as bad as it appears - it's just that despite the alliance most species still self segregate (understandably, requiring different conditions for comfort). We just see the story from the human side.
I think the question is why The Federation exists to begin with. Vulcans, Andorians, and Tellarites don't like each other, so how did they hold together a Federation before the Humans showed up? Was this entirely an alliance of convenience against Klingons and Romulans? Or was this a serious collaborative partnership that's just been cracking up as Humans arrive?
I'll say, one think I've really enjoyed about Lower Decks is that they have done more "What is life like on a Foreign Ship?" stories in a few seasons than a other Star Trek series have done in entire show runs. The closest episodes I can think of that take a deep dive into life on a Klingon ship was a few Worf episodes on TNG and Star Trek VI: The Undiscovered Country.
Your comment and the OP act like the Tellarites don't like anyone, but that's not really true. The Tellarites and Vulcans got along just fine before Humanity showed up. The Vulcans probably figured out the Tellarites' gimmick and decided that challenging each other's ideas was how they arrived at a logical conclusion. The Andorians were probably too hot headed to get along with people who challenged them on everything, leading to them being in conflict during ENT.
As for how humans fit in, humans may be crazy bastards, but they also occupy a nice middle ground between the others. We can be as emotional as Andorians one day, as logical as Vulcans the next, and a number of our political systems were built on Tellarite-style arguing. Humans can hear out one ally, then explain their position to another in terms they'll understand. We can also tell when Vulcans are secretly being driven by emotion, can leverage Andorian emotions to bring them to a more rational perspective, and debate Tellarites on even ground. Humans are the interpreters and negotiators that got these people to actually talk about their problems with each other and come to a reasonable compromise.
This whole discussion feels like nobody watched ENT.
The Federation exists because Archer was such a fantastic mediator. Add in his rapport with T'Pol and Shran, and his willingness to die in the place of a Tellarite ambassador, and it's little wonder he was able to knit the beginnings of this alliance together.
I really got an Archer vibe from Pike in "Spock Amok" (SNW S01E05), when he dealt with the R'ongovians.
The Federation is created at the end of Enterprise: before that there's a cold war going on between the Andorians and the Vulcans. The Coalition of Planets forms during the show and is dissolved when the Federation is created.
Well, the whole point of a diplomatic interplanetary body is to have a common forum of communication to soften their relationships over time, by allowing dialogue and cooperation to occur at some level in a fashion doesn't involve shooting phasers and photon torpedoes at each other. Even if the shooting still happens from time to time.
It's a parallelism with the UN. All sorts of countries who hate each other are part of it and sit at the same table, at some unequal level even. They still shoot each other and commit atrocities towards others and their own people from time to time. But still, the point is that the table exists and is available. It creates opportunities for dialogue and cooperation, that wouldn't exist otherwise, that create opportunities to solve conflict peacefully and soften their differences over time.
There's a ton of Voyager episodes of "a few crew are captured and they're working for this other set of people out here!" But those are generally not a view of another well-developed culture since they're in such foreign territory.