For what it's worth, contra to the other agreeing comments, this didn't happen to me. I'm sure this is all locally contingent upon an instructor with the ability and interest, but we had a jazz band I was a part of in middle school (in LA County early 90s) and we very much learned to compose and play music that was not written down on a sheet. I don't know that that kind of thing was feasible for the larger concert band, which had like 140 kids or something and one teacher.

I also played brass, for what it's worth, but never felt limited by breath endurance. I was a ~5:00 mile runner as a 12 year-old, though.