In my case, I've gotten through 40 years of performing with jazz groups, so in some sense I'm doing OK, but I also know that I struggle with ultra-modern jazz harmonies. This came into pretty sharp relief when I played with some musicians who were composing all of their own tunes. I reach the end of my mental map, and then I have to fake it, or improvise directly from the melody.
But I agree that "ear" and perception of harmonic structure are closely related. It's hard to describe, and might make a psychologist cringe, but a musician develops a "mental ear." And I wouldn't recommend my approach to a young player. Most people want to become proficient in fewer than 40 years. ;-) There are things I can't do. I can't compose or arrange anything worth playing. Without exception, every musician I've played with who could compose or arrange decent jazz material has a music degree.
You can't get good at any of them beyond a certain point without having your theory nailed down.
Also, a lot of jazz musicians wanted to eventually learn musical notation at least so that they could write their own lead sheets for copyright-claim purposes.
Musical pedagogy follows classical music out of tradition, but there are plenty of contemporary pieces available as well.
The thing about the classical pieces is that they're good showcases and practice pieces for the fundamental techniques of music (hundreds of years of development will do that), which you absolutely will use in your musical career, regardless of whether you're even aware of it.
The difference is that when you can read and speak music, you can read, understand, and construct music far more easily than you could without the named concepts, nomenclature, and writing system. It's no different from the power that language and writing in general confers. An illiterate person can make himself understood, but a learned person can do so much more with far less effort.
i think at some levels, of pedagogy, there's also an element of "and because it is cheap to free".
my piano teacher bemoans how we only teach music from "dead white men" (a common refrain in some parts of the internet), but is hesitant to suggest i spend money to purchase anything, instead, referring me to IMSLP for everything.
if you want music from living folks, it is still under copyright, regardless of their color or gender. that costs more.
There’s no such thing!
Also to improvise confidently you have to internalize the theory, not just understand it and memorize it at a conscious level.
I'd say "intuitive knowledge" is a good way to sum this up.