To be fair, I think there is a tier of elite institutions which primarily attract the prestige/wealth crowd (Ivy League, etc), and a tier just below them in rankings which attract the nerds who want to do hard intellectual work.
Some people take their specialization too far, in my opinion.
Highly accomplished people also often engage in "just world fallacy" thinking and consider their success as rightfully deserved due to their inherent virtue. This again is used to avoid thinking about things like the randomness, injustice, and suffering involved in existence.
So I don't think inserting yourself into a bubble of overachievers is a solution by any means.
I tend to believe that people that have relational issues continue to have them even when changing environment. Moreover, elite institutions can be competitive and it can be hard to deal with too.
After leaving school I "realized" that the universe is filled with happy morons and I have always wished to be one of them. But some day I realized that this wish makes me a moron because it's like to wish the sky were green. So actually a became one of them.
university, even the most selective ones, are just ever so slightly different to not be the home I belonged to for 7 years.