I'm always skeptical when I hear this education argument. In STEM at least, it doesn't seem that you can get a better education just by throwing money at it (ignoring the fact that a lot of rich kids don't actually major in STEM fields). You can still learn world-class Math/CS/Physics/Chemistry even if you don't go to MIT/Stanford. What exactly is this "beyond-world-class education" that rich kids get?
If you ask me, the major problem is that most people (from all social and economic classes) aren't interested or talented in activities that are productive at present (like STEM or Medicine), in addition to not being rich or connected. No amount of education can correct that, IMHO.