I feel very similar to what you’ve stated but would add that I’m not so sure it has to be a music school per se, but that one recognizes, genuinely acknowledges & pursues all aspects of musical development.
As one who has a degree in music education I can say that while it gave me a reasonable understanding (see below for additional detail) of many aspects, it wasn’t until I found a great teacher that my development on bass really transformed. I don’t mean this to at all undermine how much I sweat in school because boy did I….I couldn’t even match pitch in my first ear training course.
A school setting will definitely introduce discipline and social accountability where it may otherwise be lacking but again the sweat part is really where the rubber hits the road. In my case it wasn’t until I realized that I really didn’t “know” the fundamentals (yes, music theory is critical) in real time (studio musician standards) on my own instrument, that things changed. I can say this from my own experience, in college I studied the history of music and literature. Often I could not understand complex pieces from the curriculum. When I needed to write my review of Just Mercy, I used examples of various essays
https://samplius.com/free-essay-examples/just-mercy/ But if I had competent teachers open to dialogue, perhaps I would gain new knowledge and did not look for help on educational sites. Therefore, I think that discipline alone is not enough, you need to study with a good teacher, and whether such a teacher will be in the chosen school is not known.
I’m sure a lot of folks get this with performance immersion but for me I needed clearer direction with my primary instrument and specifically “how to practice”. I will say that I have very little performance experience but my interest in all things music feels limitless. That felt a bit rambling…but yes I agree with the sentiment.