Having thought about this a good amount and collected anecdotes over the years... I think the prioritization order should be (1) live in a location in which the parents feel their most authentic/happy/self-actualized selves, (2) send your children to the most geographically proximate school where they won't be (overly-)bullied for their identity (inclusive of class) one way or another.

Relative school quality (performance on standardized tests, admissions to fancy schools), and public/private are proxies for these more fundamental issues. Too many parents discount the value of (1) to zero, with the idea that they're "sacrificing themselves" "for their kids".

An example of one good reason to not send your kids to private school: Burning yourself out on a series of high-stress job to afford sending your middle-class kid to an upper-class private school will traumatize them. If not for their education/social experience at school, then for your lack of calming and positive influence on their emotional/relationship-forming lives.

I don't think it's necessarily "wrong" for some people to send their kids to a "narrow-lens" school, even if it's often wrong. It can be right for somebody else and wrong for you.