> they select for students that had the luck (or the right parentage) to go to either a private school or to a public school in a well-funded school district Y

> they select for students that had the luck (or the right parentage) to go to either a private school or to a public school in a well-funded school district You're not wrong, but I interpret this as evidence that the problem is earlier in the pipeline and trying to fix it here is a hack.