They don't eliminate inequality, they just facilitate a game of musical chairs. America has a very high and very well documented level of income inequality. It's also well documented that the people at the top often change. There's a lot of turnover at the top from generation to generation.

But the system property of inequality -- that is to say that American society is a highly stratified society with huge winners and huge losers -- is not going away, in fact American society is becoming more stratified. The elite universities perpetuate this system by conferring exceptional career benefits to their alumni.

Even though a few people will get promoted to the top, and nowadays some of them will even be women, people of color, etc., this system of inequality has some pretty painful drawbacks for most Americans, which manifest in long working hours, higher rates of mental illness, etc. as compared to more equal societies.