There is a growing number of parents who, because of this exact overt and known discrimination against applicants from private schools, will first send their kids to elite private primary schools and then they switch them to the best secondary state schools they can find, using the money to supplement their education with private one-to-one tutors.

This is an entirely expected outcome. Water will find a way to ground.

Oh yes, I have kids in a prep school where half of the class goes to Eton, and the rest to Winchester, Harrow, Seven Oaks, Derby... Now, for the past few years, almost no parents want to send kids to Eton. They know how much are those kids discriminated against. It's better to send them to a school with lower profile.

Doesn’t this prove the reason for the existence of the disparity? The wealthy kid’s parents want tutors to supplement the education they get from their state school.

I understand an argument saying people will game this setup, but arguing that state school kids are not disadvantaged is indefensible, in my opinion