I also think, and have observed, that state school young people who do well enough to get into a top university have proved that they can compete with the very best, just by their achievements in getting those good grades.
So many public school pupils are hot-housed and taught to the test, that when they do get to higher education institutions they find it difficult to cope and self-start.
I know this as one of my jobs is as a private tutor, and most of my students are from private schools, (Eton included), who require intensive exam preparation, which costs their parents a lot of money! Poor families just cannot do this.
My (state-educated) son had one grade less in one A level than most of the (public-school) students on his course, but his results in the pre-course exam designed to test the individual's actual aptitude for the discipline, and their innate, raw ability was one of the highest in the country.
With parental involvement (not necessarily financial), all young people should be able to achieve their potential. Universities now have all sorts of ways of finding the cream.
But of course not everyone can be the cream. And that does not really matter, as long as every young person achieves their own potential, and is happy.
The wealthiest people I know, apart from those that inherited their wealth, are entrepreneurs and trades-people who have their own companies. Several of my son's friends have gone to do apprenticeships with a view to working in the family firm, and their earning potentials are huge, as evidenced by their parent who started the company.
Due to the area in which I live, the hobbies of my children, and my private tuition I know many very wealthy people, and I can't think of one who got their wealth due to their university or degree. They all work very, very hard though, so probably that is the key to success. Along with a bit of luck. And no mental or physical health issues.