When I was 18-22 and living with my parents (pretty normal in Europe) I worked and contributed to the house expenses. I'm pretty sure kids of rich people don't do that. If I wanted to take out a loan, my parent's wouldn't be able to provide guarantees and thus the kind of loan and conditions I had access to would be much different than those a kid with rich parents could. In University people could also get grants based on your family income.

Those examples are varied and are not the same thing as purchasing a concrete product, yet I believe they are relevant to your question - education is a service that supports society, not a concrete product for your personal use and enjoyment. How and if you get it, relies not entirely on you at that point in your life, but heavily on your parents and in general on your family as a single economic unit to which you belong.