I’ve found that music education is often made way too complicated. As a teacher of the saxophone I’ve found that not many students are as well-rounded as they should be. This means that their former teacher(s) emphasized certain things and didn’t adequately address others. That’s never good.
Aaron Santee - 3 Book Jazz Compilation PDF with 13 MP3s
A teacher’s job should be similar to a doctor’s - they are to evaluate the music as a whole and address everything that needs fixing. As a student learns their instrument, they should be thinking like a good PATIENT would think - trying to be aware of anything out of the norm, such as, maybe hearing some “chirping” while playing and wondering if it’s their reed, their embouchure, their horn, etc.
Being aware of the good and the bad is extremely important for players of any style, age or playing level, and a good teacher will be able to tell the signs of bad habits forming, such as something as obvious as the occasional “chirp” sound being most likely an embouchure issue (most likely an embouchure that is too tight, “pinching”, but there are other possible causes).