Is it really as much of a necessity? In my opinion most people learn the bare minimum required for exams, and then regurgitate it. I only remember tidbits of history and a little Shakespeare from my school days. Even in college most of my professors just read off powerpoints and I was forced to learn anything useful at all for my career on my own time. Schools force people to learn things they aren't interested in like STEM over useful life skills like personal finance or cooking. I think homeschooling or self-directed education [0] could be much more effective at stimulating learners and equipping them with necessary knowledge. In my opinion the only benefit of school was the social aspect, but thats to be expected since thats where everyone else is, not to mention the drawbacks such as bullying.

Education really isn't as much of a virtue as people think; do I really need a degree to talk to people, to appreciate literature or art, to vote? (And even with the prevalence of education, people still end up misinformed or lead by personal bias) Most people are capable of learning what they need, especially when all the resources are out there and not just in schools. All the different levels of education that are established just serve as poor markers for employers to differentiate people and time-and-time again I've read about educations being ill-suited in preparing people for careers.

Like the parent commenter, I think people are quite capable of organizing and preparing themselves just as well without a state, and many communities and generations have been doing this for centuries.

[0]: https://en.wikipedia.org/wiki/Unschooling (just one interesting example)