I do not see such evidence, maybe it fails in san francisco but that can have thousands of reasons. Everything I've read here points me to the fact that the public education is not good/comprehensive enough and too inflexible. I am honestly a bit shocked what i've read here, this is definitely not my experience with public education, like not at all. San francisco is rich, people make a lot of money there. There is no excuse why public education should not excel. I bet every major politician has his kids on a private school and also every other decision maker.
> There is no way for you to create a public system that overcomes the success that comes out of parents who are involved and invested in their child’s education
This is not exactly what I said. It is probably impossible in practice to eliminate this advantage. But while impossible to eliminate, you can try to minimise it and you should. It's the only fair thing to do because kids can't choose their parents. I would go further, it's the only ethical thing to do.