European history is full of destitute monarchs and nobility. The key to understanding the elite is that they are usually not wealthy - they are deeply in debt most of the time and that is what makes them seem so successful.

To understand this simply: suppose you have lots of money. naturally people will try to take it from you and may even kill you to steal it. On the other hand suppose you have lots of debts. Your creditors must keep you alive in order to recover their money and will steer business your way because they have a stake in whatever you earn.

So, counterintutitve as it may seem, having (the right) debts will make it easier to succeed then having lots of money.

And doing so would be a net loss of value. Making people less educated doesn't help anyone.

There are a tremendous amount of public schools which give incredible educations. Much of the value of private schools is in social capital. While we can certainly point to the education levels of the worst of public schools and compare them with the best of private schools, the resume boost from a private school and the networks which are formed amongst parents and students have a much bigger impact on where a student lands than the actual differences in educations received.

Middle class, on the other hand, would happily follow cheaper rents and shorter commutes as long as the neighborhood is safe and reasonably clean. The latter two are often the problem though.

edit: they claimed to control for "skill" and inheritance (which should cover some of the genetic component) but I don't know how well as the paper is paywalled