Public education from the start was seen as a necessity for the survival of self government. It was mandated by the Northwest Ordinance in 1787. Nothing to do with the industrial revolution. John Adams advocated for “liberal education of the youth” to foster the virtues needed for a republic to survive.
Education is necessary. You can educate junior after he’s done milking the cows. He can go to a school house, and chop wood for teacher for his tuition payment, or if you have the cash, you can pay in cash. Publicly-funded and administered education is another matter entirely.