It's a big puzzle to me why this doesn't happen more often. In the past it did. Fighting inequality or discrimination, especially at the professional level, started when someone said, "Okay, I'm just going to make a school for my own then." My favorite example of this is the dismantling of Jewish exclusion at New York medical schools, which happened by creating new medical schools that did not discriminate. [1]
The idea that prestige is entrenched, basically, is wrong. Maybe that idea is the main obstacle to education reform.
Although maybe this is already happening for rich people. Alt Schools come to mind, although its story has come to an end.
I don't think it's possible for the superrich, as a class, to guarantee admissions for their kids at elite universities, because there's only so much space. So why haven't they built their own school?
[1] http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC18080...