Without bothering to provide any citations, I'll take the challenge of explaining "free public education."
At one time in this country's history the idea of sending a potential farm worker off to some place in town to learn useless stuff like reading more than the Bible (an oversimplification) and how to cipher the farm accounts was deemed wasteful at best.
As the number of folks living in those newfangled "cities" increased, there were fewer opportunities to keep the rugrats off the streets and out of mischief (not quite as much of an oversimplification). At the same time, those rugrats that managed to arrive at their teenagehood were discovered by many potential employers to be less than useful because they did not know how to do much more than cause trouble and hold up walls. These newly emerging teens were, BTW, looking for employment because their parents were no longer willing to subsidize their existence without some return on investment.
The town fathers and the major employers got together and dreamed up "schools" and the concept that it would be better for everybody if rugrats were sent there.
At first these "schools" were private, for-profit enterprises. But as westward expansion happened, the free land crap in the Northwest Terrortory [sic] came with the pricetag of a parcel of each section being required to be set aside for the creation of local government. The folks who became the local government decided they needed to have stuff to do besides collect taxes and hold 4th of July picnics, so they decided that they could intrude in the lives of just about everybody by decreeing that the town would go into the business of schooling kids. Even if you never spawned a kid you were impacted because you had to pay taxes to support the schools - if was, after all, for the children. [There is speculation that was not the first time the phrase was used in America.]
Folks were too busy running their farms or trying not to trip over idle rugrats in town, so they pretty much went along with this newfangled plan as long as the kids could be sent out to the fields at harvest-time [now called "summer vacation" and slightly time-shifted at the request of the amusement park operators].
Some folks say the idea really came as an offshoot of Franklin's concept of every town needing to have a free public library so folks could edumacate themselves about stuff, and read up on politics and the like, without having to pay a penny each time they walked in the door of a private library. [Franklin figured if you collected the equivalent of two cents per visit, but in a lump sum at a time when folks were bitching about all the other stuff money was being collected for, they would not see the scam for what it was. Franklin got the idea from the previous rulers, who thought "taxes" were a gift from the gods.]
Anyhow, it was "for the chilllllllllldrennnnnnn." That being the case, it was a good thing to do.
OK, class. Civics is now over. Take out your slates and flints, because we are going to practice ciphering. Tommy - if a farmer buys a bushel of wheat at thrirty-five sents a peck off a train moving at 75 mph that left Cleveland at 6:30 last night ....
stay safe.
skidmark