Okay, i see your argument, but what do you suggest?
Every child who attends a private school has parents who pay tax. Therefore they are entitled to a state school education.
So you shut all private schools, and all the children move to state schools.
The state schools then have a load of new children, with little extra funding for the new pupils. the only way to meet that is to increase the education budget and that's a bit tight already..
Bigger classes, but no money for new desks, or teachers, or books...
how would you solve that problem?