I'm reading a fic - Stargate, post reveal, though it could apply to any SF first contact story:
"Wars over stupid things like land or oil or religion had to stop before someone or something came along and picked us off while we were squabbling amongst ourselves."
And that sounds shiny, sort of, but it misses a lot of the point of why wars happen. Maybe boss people go to war far away for an extra slice of pie, but for most of history there's also wars that are just about survival. Land equals survival, on account of needing food and buildings and all sorts. Oil is kind of essential these days. And religion, to the true believer, is absolutely about survival, not just in terms of the eternal fate of their souls, but in the day to day saving of the righteous here on Earth.
After first contact, I don't believe the whole Earth will do anything all at once. There's seven billion of us, we're going to have seven billion reactions. Some of the people will understand the new data in terms of the old, and for some of them that means the war in heaven and the very real and physical presence of demons, or other intelligent life with an inherent moral standing. A LOT of people will hear there are whole new worlds out there, while they and theirs are starving down here, and they'll decide their only chance of continued life is to get out there. If they believe America's control of the gate is absolute, then America gains a lot of control on Earth, but that's not how a lot of people respond to American power in the here now. Even if governments all agree to America's terms - and shyeah, right - there will be smaller groups who think the system is corrupt and the only way to achieve freedom is to attack the system. Hence 'freedom fighters', or terrorists. All of which ignores that some people will want something to come along and pick us off, for reasons many and various. In Stargate especially this entire galaxy was controlled via myths and the old gods, with Goa'uld and Asgard both playing. Why would that suddenly break? Science? Science can only prove how god is doing it, not that god isn't doing it: see Intelligent Design. The assorted monotheisms would have a large something to say about a resurgence in the kind of polytheisms exploited in the Stargate 'verse, but how would they respond to Ori? It wouldn't be monolithic, and where there are disputes there are conflicts and there can be wars. Plus there's people who think humans have screwed things up enough someone else should have a go. Or people who reckon they can profit from it. All sorts of reasons.
Humanity is not going to respond in one unified way, and there's nothing in the near future that leads to universal peace. Even if there's some tech development to get us to a Star Trek like post scarcity future, ideological differences have fuelled wars enough and can fuel plenty more.
But it's the main thing I never could buy about Star Trek without imagining frankly scary intervention of technology, that humanity all held the same opinions now, and were happy to.