Elite private schools in SF and NY are closer to 40k/yr. Catholic schools tend to be much less, with elite high schools in the 20-25k range, though it’s not an exact substitution. Catholic schools teach Catholicism, and while students are not obliged to be catholic, they must attend religious services. The catholic 20k tuition schools also tend to be larger than independent elite privates, though many of them are reasonably elite as measured by sat scores and colleges attended.
This all supports your point, other than to say it’s even more expensive than you’ve indicated.
This all supports your point, other than to say it’s even more expensive than you’ve indicated.