Sorry SUSSA . . . meant to ping you too!
No problem.
Jefferson did indeed propose a government school system. It was rejected by the other Founders. Franklin went with a capitalist system when he started the school that became the University of Pennsylvania. He put up some of his own money and got other well to do citizens to contribute the rest. To this day the University of Pennsylvania is a “private” university.
You’re right that neither Jefferson nor Franklin, nor any other notable Founder, envisioned a single payer system of government indoctrination centers. It wasn’t until the 1850s that government schools started spreading through the States.
Prior to that, the vast majority of schools were funded by parents and local wealthy patrons. Frequently, “schools” were rooms in back of a store or the parlor of a large home, or a church. The teacher was paid by the parents who decided to use the service rather than take on the task themselves.
Police and courts require the power of government to do their work. Police and courts require the threat of force, and occasionally use of force to do their work. Schools, healthcare, and fire protection, do not. Many towns have volunteer fire departments that do a darn good job.
In the case of schools forcing people who do not want to be there to be there by force harms the work schools are designed to do.