So, at the risk of gross over-simplification from these *very* rough estimates: factoring in the opportunity cost of capital, families with one child would be financially better off sending their child to private school than splurging on a house in a competitive school district, all else equal, in many parts of the US.
This may be an especially important realization for families with a gifted child, as government schools are increasingly focused on equal OUTCOMES, and may not offer gifted children learning opportunities and experiences with appropriate challenge in their zone of proximal development (ZPD), and with intellectual peers.
Unfortunately, in following the links from the OP's post, some of the wide range of materials appear to suggest a goal of equal OUTCOMES also at this private school... or even a ceiling imposed based on race/ethnicity... specifically shaming white pupils based on the color of their skin.
In selecting a school, parents may need to look beneath the surface and beyond past admissions history of a school's alumni.