I would be perfectly fine with the current schools staying open, so long as they have to compete with other schools for the per-student vouchers or similar a reformed system would have.
They'd have to get their shit in order or go broke real quick.
If you think there's remotely enough private schools or charter schools to even ATTEMPT to replace public schools, you are flat out disconnected to reality.
Sure, private schools are technically 25% of America's schools... but they only serve 10% of America's students.
There wouldn't be remotely enough supply for many people to switch.
Also, because of the voucher system and because of people interested in switching who do now have the option, the price of private schools would likely go up.
Its also worth noting that the percentage of American students in private schools has been declining; from 1995 to 2021 there was a 20% decline in the percentage of students in private schools.
Beyond this, 78% of private schools are religious, meaning there is a lack of secular schools, which is what quite a number of parents would prefer.
Any sort of belief that a pure per-student voucher system would result in a massive win for private education and a loss for the public school system is pure wish fulfillment fantasy.
It also ignores that both Private and Public schools have a ridiculously large range of quality, with Public Schools ranging from "Upper Middle Class Suburbs with 8 digit facilities"* to "you have gang wars in the hallways," and Private Schools ranging from "literal memetic boarding school for the super elite" to "the education is a joke and the teachers were just desperate for any job."
* The schools of the real upper middle class are very different from the schools of the proles.