Here in the UK the educational system is equally stratified. Now, it is true that excluding the very few admitted for sporting prowess (rowing at Oxbridge) the typical student at an elite University is of a higher calibre than the typical student at a non elite University. This is due to selection.
BUT, children of the affluent are able to access much greater educational opportunities than children of less wealthy parents. This means they have a better education and are better prepared to pass the entrance procedure at the best Universities, while equally capable but poorer children are disadvantaged from the outset. However strenuously denied, the suspicion that "people like us" are being selected is difficult to avoid.
I went to a second tier University where many of my fellow students were affluent but not good enough for an elite University. Even then it was clear that their life experience and future expectations were vastly different to my own. I have, I believe, succeeded on my own merits in the UK tech industry but even so I have ended up financially and socially below where the affluent kids started.
In a class based society birth and/or wealth are a far greater determinant of life success than talent or any other attribute. In this, the UK and US are identical.