It wasn't free, they were taxed for it. We also have been historically taxed for poor houses, county farms and asylums for the indigent.
If you didn't want to live there you paid for own and if you didn't want to have your children educated in the government schools you paid for your own.
If a “private school” becomes a virtual clone of public schools, that will be apparent to well-informed parents, who can avoid that school.
I guess we'll just chalk that school up as a casualty of egalitarianism. No thanks, I've seen enough casualties of egalitarianism through government.
The system we have is corrupt and ineffective.
Most of the private schools are fine. If people can't afford it, that's life. You get what you pay for.
It is sinful, in fact.
What's sinful is redistributing even more money through the school voucher system to people who already aren't net taxpayers.
Your solution: keep as the primary practical option government schools that are absolutely controlled by centralized government bureaucrats, and that indoctrinate students and provide a shitty education.
Voucher sulution: return local citizen influence to local public schools by giving parents a direct choice that will force government schools to adapt to the educational needs of those they serve, rather than dictate to those they serve what their needs must be.