Privatizing schools wouldn't help as much as you think. Public schools operate under the influence of state mandated quotas to increase graduation rates and scores. That gives rise to reducing standards and tolerating bad behavior in order to retain students long enough to graduate.
Private schools would be judged by the public with exactly the same criteria, and would consequently develop the same forms of rot.
The problem with public schools is actually the public. Parents don't have high expectations for their children with respect to behavior or academics. Most students are difficult to teach and tend not to care about anything but electronic gaming a social media. THOSE are the root problems, not the schools.
1) In every study where children who were accepted by lottery to receive a voucher or attend a charter, are compared to those who weren't, the children who attend the private school or private run charter far exceed those children who don't. But...This isn't my main reason for condemning compulsory government schooling.
2) Fundamentally, government schools are NOT religiously neutral in content or consequences. ( Read the Barna studies.) All government K-12 schools are godless in their worldview by law. ( Yes, **all**) Children in these godless classrooms MUST learn to think and reason godlessly if they are to cooperate in the classroom, do their godless homework, and read their godless texts. How could it be otherwise?
3) The government ***compels** children to be in a prison-like setting where every First Amendment and human right is trashed by the government and its toadies ( oops! “teachers”). The children are at risk of learning to be compliant prisoners of the state. Perhaps the reason so many Jews sheepishly boarded the Nazi death camp trains was due to their compulsory government schooling!
4) It is impossible for any government schools to be religiously, culturally, or politically neutral. Such a state of neutrality is impossible in the mind of any sentient human. Therefore....Government schooling is a First Amendment and human rights abomination.