You’re describing Finland. They outlawed private school funding for exactly the reason you’re proposing: to get the wealthiest and most engaged parents invested in fixing public schools for all.
It worked. They have one of the best public education systems in the world.
This is a big oversimplification. There are many differences in education between Finland and the US. Pointing to a single one and declaiming it as the cause is unjustified.
As a counter example, the OECD PISA ranking for education puts Estonia as just barely ahead of Finland[1]. Estonia has public and private schools[2]. So, it is at least possible to have Finland quality schools while maintaining a public and private system.
Another thing to consider would be the population differences. The US has ~65 times more people than Finland. In this larger group of people there will be Finland sized subgroups that outperform and underperform Finland even though the US as a whole underperforms.
Massachusetts, for example, one of two states in the US to perform and report their own PISA numbers, is pretty comparable to Finland in 2015 (1 or 2 points above or below on scores of ~500 for science and reading and 11 points below on math)[3]. I couldn't find the official OECD results for 2018, but I believe Massachusetts is slightly ahead by then.
It’s a Finland solution to a Finland problem. I don’t intend to suggest it as anything more. Only to show the parent commenter that his/her idea is not so radical; there’s precedent elsewhere in the world.
It's cultural. A school system can only be effective up to a point, but depends mostly on the stock of students/parents involved in the system.
You'll see MA scores among the top states in most forms of human development, so it shouldn't be surprising that the schools reflect that trend. The MA school system is likely not doing anything particularly unique that will be the antidote to failing systems in other states. It's likely the best way to replicate their success in other states lies in policy not directly related to school systems.
It worked. They have one of the best public education systems in the world.