It probably is something that makes sense when you've experienced it. There's a certain quality about camp as a place that's detached from the rest of your life and temporary that allows one the freedom to be themselves - or maybe more importantly, someone else - because the consequences for fucking up are inherently limited. You don't have to worry about your parents or your social status back home, no one knows about the time you peed your pants in school. Plus a lot of camps do stuff that breeds camaraderie but are unusual for normal life. Singing at mealtimes, cabins having projects to be done over the whole period and shown off, and other ways for kids to feel like they're part of a group. And this gets reinforced by the aforementioned safe space to figure yourself out. Because the consequences for oversharing or whatever are limited to the time that you're there, kids often allow themselves to be more vulnerable and talk to their peers about embarrassing or difficult subjects. In general I just think that the particular nature of a camp as separate from everything else is what makes it so valuable for youths development.

Kids socialize on their own time and in their own ways.

Not these kids. Your other points I agree on. It's just like watching the last bricks be put on a wall lmao.