And yet those kids from state schools then come out with more firsts than those from independent schools, showing they were not “dumber” at all - they were smarter.

Really, oxford and cambridge as well as other top universities can have a simple algorithm. They should bias against those from private schools in terms of admissions criteria until the point at which outcomes (as measured by graduating degree scores) are equal. This wouldn’t happen though because then private schools would drop to 5% of enrolments and there’d be no advantage gained from paying for a private school education. Unthinkable!