- Edited
I have been asked many times in the past if I can teach them to play piano by-ear, and improvise. I refused to teach them. Primarily because I am not capable of teaching it. I have no pedagogical background in music whatsoever, I just do most things intuitively. Teaching others my style would be a disservice to the student.
On a separate note, I've found (in all sorts of industries) a halo effect, where folks think someone would be a great teacher of their craft, primarily because they're excellent in doing the craft. But teaching/coaching versus doing are distinctly different. They may at times overlap, but it's not always the case.
[some random analogies] I think of various NBA Hall of Famers, who went into coaching basketball teams, and the results are hit or miss. Michael Jordan, phenomenal as he was, wasn't exactly the best in managing/ owning a team, etc. Or take University and colleges, where a world-renowned professor teaches by death-by-powerpoint. Likely, they're in their tenureship due to research credentials and not ability to teach effectively. The most effective teachers in college to me were adjunct professors.
And I personally (if I was an aspiring student in classical piano) would prefer to learn from an esteemed piano teacher than someone like a Yuja or Martha or Daniil or whomever. Perhaps they could teach well? But I have no evidence of that.