An idea that may have merits so long as a feasible alternative can be proposed but surely not the best place to start when trying to increase the liberty of the country or convince others of the merits of free market and a limited republic. There are so many other egregious violations or liberty (e.g. banking, government spying, corporate lobbying, bailouts, military industrial complex, gerrymandering, gun bans, TSA, free speech zones, militarized police, ...). And talking about abolishing public schools is a quick way to get marginalized and written off as a quack by 90% of citizens. Probably better strategically to focus on areas where there are at least allies and the battle is winnable.
You'd have to ease people into it for sure.
Start by abolishing the Department of Education. That's something Republicans have talked about many times (But do they, when they have the ability). Return all education choices to the states.
The states could then kill their Department of Education, giving power to the county level. Now citizens could be given a huge portion of their money back if a city decides to remove education from their property taxes. This would appeal to many.
other egregious violations or liberty
Those are good goals too!
DoE definitely should go, and I think it would even be politically feasible if people understood that would mean more local control over schools. But most people think DoE == public schools, so even abolishing DoE scares away most people.
Yes, it has been a Republican talking point for years (much like repeal Roe v. Wade), but I think it is merely a ploy to fire up the base; they will never actually deliver on it since it is politically unpopular. I try to stop listening to what politicians say they will do and focus on what they actually do. Republicans seem to focus instead on pandering to corporate interests when they achieve power.
Yet another reason public schools should be abolished.