Well, you have Montessori and Steiner, both alternatives to the factory schools. I don’t think homeschooling is the way to go for all of us. My main concern would be the social learning, not all families have 4+ kids. 

So what’s the main problem in modern schools? In my opinion it’s the lack of practical and creative subjects, not enough physical activities and playing (especially for the youngest), and the fact that most boys would have been better off starting school at a much later age (7-8y). And last, but not least: Music and singing is heavily underrated as a tool in almost all subjects. It’s a well documented fact that singing boosts endorphins, builds the sense of belonging to a group, helps you develop language etc. 

(Disclaimer: I’ve been teaching vocal arts and music production for 15y at high school level.)