Fuck public schools, but there is a flaw in your logic when applied to broadly. There will be other systems that centralize power, and will eventually overthrow your libertarian system because it lacks an overfunded, organized military. So centralized power is a necessary evil. The problem is that the present centralized power is a bunch of devil worshiping pedophile sociopath bankers. I like the idea of dark libertarianism, where the libertarians form a military and crush anyone who threatens their system.