I attended one of the worst secondary schools in the country. Less than 10% of my year earned the qualifications necessary to go on to university. I know that many of these people, who have gone on to be successful in life, would have excelled at an independent school and would have excelled at university. They were in poverty, not stupid.
You cannot compare the achievements of a student at an independent school to those of a student at a state school based on grades. State school and independent school are a fundamentally different educational experience.
If you think Cambridge and Oxford exist to accept the highest graded students in the country, rather than to accept the students that have the most academic potential, then sure, let's only admit students who have 3 A*s.