You make a good argument about the class differences in education, and thus opportunity. But in one respect, all classes (at least in the USA - I'm not as familiar with other countries) suffer from the same defect, a defect which itself perpetuates the class system.

That is the obsession with testing and grades. Those tests, which are the gateways to higher education, have been proven to be racially-discriminatory. But getting a "neutral" test (if such a thing exists) won't solve the problem. The very nature of tests is to assume that there is a "correct" answer to every question. So our "education" has become a system of memorizing the "correct" answer and regurgitating it on demand. The natural curiosity and critical problem-solving of children is suppressed, replaced with a "test" of obedience and conformity.

We are, and have been, preparing generations of children to be obedient and to never question the system they live under - whether they are workers or capitalists.

We seem to have already arrived at Mike Judge's nightmare of "Idiocracy."