Perhaps rich people are getting the result they believe they are supposed to receive? As in, their behavior is modified in minor ways they do not perceive but all towards the goal of increasing the success of the children they enroll?
It really comes down to parents. Children are not autonomous for the early formative years and how the parents treat them, from setting their morals and encouraging good behavior sets the course for most of their life barring abrupt unforeseen external forces.
I have only one issue with private schools, I do not believe any politician should be allowed to send their children to one.
So, they need to sleep in the bed they make. If they don't offer parents the choice of what schools to send their kids too on the basis that their schools are perfectly fine then why don't they stand behind their words and send their own kids there.
Yes I support vouchers, I think schools should have to compete for the money. The money needs to follow the student, not the school. In the nearly forty years we have had a Department of Education the only thing that has gone up is the cost per pupil, scores certainly have not.
I could totally believe that it's totally irrational on the rich parents' part: kids and health are places where people lose much sense of rationality and perspective. But it's still worth considering that the people who are typically most invested and knowledgeable about their kids and the benefits of a good education do usually go for private school if they have the means to.