There are people who don't pay school taxes, and not much income tax. They would not be able to provide any form of education for their children if all schooling was accomplished through private schools. Public schools were actually established with those people in mind. Ponder for a moment and think of the Dark Ages, Medieval Europe, or most any period up to modern times. The only people to receive an education were nobles or the otherwise wealthy. Are you advocating for a return to that situation?
How about we just fix what the liberals screwed up?
Public schools would be in competition for tax dollars that will follow the student. Are you arguing for an end of FedX and UPS because they provide competition to the government postal service? Public schools will have to up their game, they have been providing poor education for decades.