I have to say this is probably the first time I've ever seen someone argue that public schools have always worked and are proven, and that by contrast private schools are prone to have quality issues.
The more usual thing you hear is something like [0], which is something I can't personally attest to or anything, but I've seen it expressed on places like /r/teachers as well. If true and at all common, then that sounds to me like public schools have given up entirely.
If we try to reinvent it like with charter schools, then we need endless regulations to prevent scams because people are greedy and act in bad faith.
Rather than make government huge and try to prevent tax grift, we could just have what's always worked and is proven.
Why are we shifting toward private schools? Because of regulatory capture.