No, but they still make us pay for public schools, whether we use them or not. Until that changes, private education is a much larger financial burden than it would be in a free and fair market.
They make you pay for roads you don't drive on, prisons you don't live in, police and fire regardless of whether you use them or not. I don't go to the local university but I pay for it. If you don't choose to use the public school system then that's your right. Send your kids to private schools, home school them, or send them to public schools. That's your choice.
My parents "paid for" public schools, even while sending me to a private one. My husband and I "pay for" public schools, even though we never had children. And I don't recall my parents, and certainly not my husband and I, doing all the whining about this that I see on this thread!