Honestly, how many kids do you think would choose to study anything if given a choice?

While not perfect, Montessori seems like a good start to demonstrating that kids can choose to study.

The Montessori Method of Education, developed by Italian physician Maria Montessori, is a child-centered educational approach based on scientific observations of children. The method views the child as naturally eager for knowledge and capable of initiating learning in a supportive, thoughtfully prepared learning environment. It attempts to develop children physically, socially, emotionally and cognitively.[1]

[1] https://en.m.wikipedia.org/wiki/Montessori_education

I think of Montessori as a smart middle ground between under-structured "child-centered" and over-structured traditional education. I've seen it explained as a triangle of child, teacher, environment, where the teacher spends some time preparing the environment, some time instructing the child how to interact with the environment, and some time making adjustments to the environment.

Love Montessori. Have you heard of Sudbury Valley schools?

I learned 95+% of things I know about programming outside of class. Now, I doubt that anyone would really lean a "well balanced" set of subjects, but students can be made to have their own intrinsic motivations to study things.