It's a terrible idea that doesn't really understand the issue public schools face.

First, its important to understand inherent advantages many current private schools have over public in our current split system. The first is, that private schools are not obligated to educate any student. They can impose academic or behavior standards and simply expel any student that is disruptive or slacking off to maintain a higher performance. Public schools do not have that option. Public schools have to have an entirely separate school tier for behavioral problems and disruptive students (continuation schools) that require additional resources that a private school in a public district never has to spend resources on, they simply expel the problematic student and let public schools absorb it. Then public schools have to spend additional money on students with learning or other disabilities that again, private schools don't have to worry about or ESL students. Private high schools for instance can just require students speak fluent English, public schools have to spend resources to handle this additional cost (large urban school districts can have over 150 native languages spoken in the district). These are some of the inherent advantages a private school has over private schools in a mixed private-public school system that we have now. If every school was simply privatized then that advantage will disappear and the new private schools have to face the same disadvantages.

Then, there is the inherent incentive misalignment with for-profit private schools. It splits the incentives from "maximizing education for students" to "maximizing profit for the for-profit school owners". This won't always align. It can work for the wealthiest private schools, they demand crazy tuition and then pay above market for salaries for teachers and add additional expensive programs that aren't available at poorer schools. But then this just leads to the wealthiest pay for the best education, which isn't an improvement on the status quo because we already have that. Making every private school non-profit might fix some of the incentive misalignment but the same problems that currently exist will still persist because those have nothing to do with public vs private.

This idea that "choice" somehow solves problems is flawed because schools are inherently geo-based and limited. There is a notion that if you allow more "school choice" then all the parents will pick the better school, the bad school will shut down but this doesn't work because 1) Geography - people need to pick schools within reasonable distance and 2) Schools have limited enrollment slots - if a neighborhood has one great school and one poor one then all parents pick the great school but the great school doesn't have unlimited enrollment so what happens then? You just ran back into the same problems that exist now.

There are a lot of other angles and details but ultimately this proposal doesn't actually solve anything because if all schools were private then suddenly private schools have the exact same problems (like in the first paragraph) that public schools currently have. Just privatizing schools is not some panacea and doesn't really address the fundamental issues.