I don't think there is anything you can do to prevent rich kids from having an easy life.

They are not numerous though, but definition. So the concern shouldn't be too large as well. In France where i'm from, and also here in Japan, i see the education system as mostly working. People get educated and the people more designed for more study can pursue while other go working before them. This seems to work enough to me. I wouldn't know how to improve it without regressing more on other fronts, for instance