Your thinking on this is factually incorrect. If you're middle class or worse, and have the smarts, you can basically go to any of the top Ivies for free these days.
I had a pretty good shot of getting into an Ivy League school 10 years ago(4.0 and highest SAT score in the county), but I didn't apply because I thought my parents couldn't afford it.
That doesnt change the overwhelming competitive advantage rich families have when it comes to prestige schools.
Many wealthy families sink tens of thousands of dollars into preparing their child for university admissions - an advantage only the most brilliant middle class students can overcome.
Even then you have to ask yourself what it means to attend a prestige school. Are the students honestly getting a better education? It's not like they use a special set of books reserved for prestige schools only, and I have a hard time believing slave-labor TAs teaching skills would be any different at such schools.
I'm not sure about how true this is in the US, but it's definitely much less true for international students, a group that YC doesn't want to leave out.
I had a pretty good shot of getting into an Ivy League school 10 years ago(4.0 and highest SAT score in the county), but I didn't apply because I thought my parents couldn't afford it.