Individual parents, families, grandparents, aunts, uncles, older cousins, neighbors, and......churches.
Remember: Millions upon millions of Catholics were educated though personal donations to their parishes and through the work of dedicated **volunteers** ( AKA nuns, brothers, and priests).
And....Any child who is educated today is being either homeschooled or after schooled by parents, friends, and relatives but the government school will eagerly claim the credit for all the hard work done in the HOME.
I personally go twice a week to teach my grandson Saxon Math. Of course if he attended government school the school would take full credit for his being 3 grades ahead of his peers.
In a perfect world, mom or dad would be home to spend hours after hours teaching the child. Not in our world today. Millions of both moms and dads have to work to make ends meet. What if mom & dad have a marginal educations themselves. Have to pay tuition to attend parochial schools and Christian academies. I know, paid 12 years of tuition to the local Catholic school system, it wasn’t cheap. It was worth the money though, and I could afford it. Not much money, little chance of a good parochial education, it is not free. The church schools and home schooling are viable options for hundreds of thousands of students every year, no doubt about that. But there are millions of children that require education every year, your model will not work on that scale. Public schools do work, when managed at a local level and reasonably funded.