“the opportunity to develop relationships with those on their level. It’s extremely important to their development and even to their happiness”
Seems to me that that is a good reason for parents to put their kids in a HS situation where they fit with their peers. Those families that would be full-pay at a private would be able to afford that. I’m of the opinion that spending money on HS is more important as an intellectually top kid would be able to find peers and opportunities that suit him/her for free or close to it at the college level but that is less likely at the HS level unless you are in the district/state/city of a top public magnet.