Is it off topic? The topic is the role of theory in making a good player. We are discussing how that applies in different genres.
You are right that the theoretical underpinnings of Mozart differ from those of Stravinsky. Surely the same is true of different jazz genres. Then there's a whole different mindset to play good folk or bluegrass. Great classical players may be able to nail the notes but not the feel.
I would say this... in general I can say this about different "anythings" eg. different people, different genres of music, different cuisines, different languages, etc. i can say "Different ( fill in the blank with any category of a "thing" eg genre's of jazz ) genres of jazz, are actually BOTH very different from one another and of course also have much commonality. "
So a dichotomy is ever present.
Common aspects are:
For instance PITCH, regardless of the genre of music, pitch is a constant. In contrast , Dixie land jazz is rhythmically much more earthy, more basic, more tied to 1 2 3 4 than say, Avant garde Euro improv.
My point is "things" are not JUST different, or JUST "all the same" ( as I so often hear - "we are all the same" or " music is music" ) but actually they are a blend of very different aspects and identical aspects. Again, an identical common aspect such as steady tempo, or fairly consistent pitch control, or bass player ( Tuba, piano, pipe organ, string bass, bari sax, ac bass , bass trombone, bassoon ) playing bass notes, playing the Root of a chord on a downbeat, often at the beginning of the bar.
In our society, I hear much too much of the argument that all things are the same, and variations of this nihilistic idea. I may not be clear here, forgive me. Just maybe think about it, and I will hopefully add more clarity, as the ideas come to me.
This is not off topic, I relate it directly to the cardinal question, "WHAT theory, and HOW MUCH theory is enough?".
To your question ( fingerbun ) what is the role of theory TO MAKE A GOOD PLAYER, I would say that is old school 20th century thinking. I personally like it. But I am rethinking it. I say, it depends on the player/ student. Remember, all people are the same AND they are also QUITE different. If ALL people are given the same diet, there will be some bad reactions. For the O poster to ask the question he asked, hints to me anyway, that he has subconscious resistance to theory.
This suggests that different versions of theory ought to be taught.