Remember, the public school system that we have today - by in large - is the construct of a former US Congressman and Massachusetts' legislator/educator named Horace Mann. Mann wasn't even born until close to 1800, and his public school theories weren't even articulated until well into the 1830's.
I'm not sure if I'd agree "all the founder supported public education". I'm not sure if any articulated a system similar to what Mann advocated, FWIW.
Vouchers now! No tax dollars to fund anti-American anti-Christian schools that burn money and produce pathetic results.
No, I go back to 1770-1800, way before Mann. They ALL, every one, supported public (i.e., government-funded) schools as opposed to “private” or religious schools. At the time, there was no such thing as a private secular school. Benj. Rush said if people can’t agree to fund schools, then there is nothing worth funding. I can’t find a comment by Jefferson one way or another, but I found statements by almost every other major Founder in favor of public schools. I wish it were otherwise, but the evidence is the evidence.