Well, first off, summer camp answers the question wtf are the kids gonna do all summer, for at least part of it. So, if you have the means, it makes perfect sense.
Then once you get to camp, it has the social aspects of any other elementary/middle school organized activity. Kids are capable of turning it into a greater or lesser shit show, as are their parents.
Through the 70s and 80s, even at my ultra-privileged, ultra-white school, it was just something you did, guided in some cases by family tradition. It wasn't some status competition like sorority rush. That seems to be a more recent development that is sort of symptomatic or emblematic of further polarization and wealth and privilege concentration.
Like, my friends that were close with what apparently was the prior generation of the Eastland family (owners of Mystic), were close because Mom grew up in Hunt on Highway 39, basically across the street from Mystic. She went to Tivy and Tech. Her husband was from Lamesa, for fucks sake. Granted, both families were well off, but solidly upper-middle not oligarchs.