Restaurants have inescapable standards to meet - the public's.
Failure to meet those standards means resources quit walking through the door, and the entrepreneur who cannot manage resources to satisfy the public quickly learns the public will bring them no more resources to manage.
Restaurants fail to meet public standards at an amazing rate, and firms fold and new ones with new management and ideas to satisfy public demand spring up to replace them.
Profit/loss is the measurable and inescapable audit facing every private concern out there that exists to fulfill a public demand.
Satisfying pubic demand, evidenced by winning consumer support, is a requirement that doesn't apply to public schools for no apparent reason.
Make them compete, it's the only way to weed out bad ones. You acknowledge above there is no weeding out under the old model. That is a serious flaw.
I'm willing to walk you through it, but you have to answer first.
Do you 'cost' someone else money if you take your business elsewhere? Do they somehow own your business? Or do they have to compete for it, to your exacting standards.