No one will "become Bach" by attending a school with good music curriculum, and no school could have input a Bach-level talent and output a median musician.
And when he was 15, he went to prestigious school.
Also, classical music in general involves a lot of theory. It is not just about "make nice sounding tune by intuition".
Youtube has really opened my eyes on the subject as well: there are truckloads of jazz players discussing musical theory.
Which makes a lot of sense in hindsight: properly deconstructing and playing with structures is difficult if you don’t deeply understand those structures. But I’m not really musically inclined and I’ve never been fond of jazz so I never saw this.
But to play folk or rock music for example, you do not need that much of it. If you can read music sheet, you can reproduce the song. You can kinda create similar own going by intuition. But, creating the stuff Bach was creating absolutely does require tons of knowledge.