Cultural homogeneity and, yes, race, have a lot to do with that
Wealthy Utahns send their kids to public schools because, for the most part, those kids will still be at a school with kids of the same cultural and racial background.
I live in a place where 99% of upper clas professionals (and all of the 1%) put their kids in private school. And the main purpose for it is to insulate their kids from people who are culturally and, yes, racially different.