As you say, what matters in music is how you play and many great players have little or no formal education. It may be more formal in the classical realm, but a listener will not care about your qualifications. But people will do it anyway for various reasons. I went to college to study engineering where you do need that structure. I do music for fun.
It is more formal in the Classical realm... definitely, but I find that there is also a preference for things that are quantifiable but ultimately... meaningless. It is like training musicians to be mindless robots...