I studied music in college, with the goal of being a high school band director/music teacher. I never went into the field though.
The following is my experience/observations - not necessarily fact. Take it for what it’s worth.
The whole “those who can’t do, teach” idea doesn’t apply. I can and was doing it as a professional musician (performance) for a good while. But I wanted to settle down and raise a family. That lifestyle isn’t the best for families. I wanted a steady, reliable job with the health plan, etc.
Music students, professionals, etc. consider themselves as artists. Even the HS band director. The performance is the culmination of that artistic endeavor.
In addition, arts programs and extra-curricular activities like pep band, marching band, etc. are usually the first programs to be cut when the school/district has funding problems. Many people perceive music/arts to be nice to have, but not necessary.
Thus many band directors have a sort of chip on their shoulder plus something to prove. They constantly need to justify their existence in the school so that their program isn’t cut or eliminated entirely. My college coursework included learning ways for the band/music teacher to advocate for their programs to help avoid cuts from hitting their area/department. We even had to draft speeches/arguments in the context of presenting to school boards, PTA meetings, etc.
Math, science, english, etc. doesn’t need to justify itself in the public school. And in order to keep your job as a teacher in one of those subjects, one really only needs decent test scores.
With music/band, the performance is sort of how that teacher is graded by the administration. In a way, the band director’s job is on the line.