well to me it appears that school is a necessity till pre-teens just to get the basics done(because there is no way you will be able teach yourself at this point) but it is essentially way too inefficent so I would say that the best way would be to study on your own while in school and leave it as soon as you have some topics you are absolutely fascinated by. Attaining knowledge requires a lot of discipline which is impossible without motivation and at the very least school does provide knowledge to people who are not interested as they will not be doing much otherwise. Honestly, it is far more practical to study on your own as long as you know what you are looking for.
All kids are naturally curious, but kids usually stick to things they like, which mostly are things they find fascinating which are in turn things they usually like and those are usually things they can best understand. I am not btw saying its bad idea to teach people something important, but generally people just dont like it which means their performance is bad.
What I think is the major problem is how things are presented in schools and the other issue is narrow choice of subjects.
For example you can study history, but there are so many ways one can study history.
You can study history of science, technology, fashion or anything.
But we are always stuck studying one thing and that is popes, kings, and magna charta. I mean wtf? What kind of kid wants know that and can understand it???
Similar thing goes for any other subject. Physics can be studied through math and equations, but a lot of simple physics can also be demonstrated on various models and they would prove very useful as most kid have trouble grasping the abstract equations. However you can show kids a model of lever and show them how it works and suddenly everyone gets it.
Math can be fun. But the way its taught is really boring. I mean I used to be in math classes and we had extra math, but it was just drilling and doing the same shit. They suck all the fun out of these subjects and make it fun only for small percent of students that are inclined to study things in that specific way.