Are there really embouchure problems? Can’t air fix all of them?
Proper breathing IS proper breathing. It does not matter if you learn from a sax player, tuba player, singer or even a trumpet player.
I say proper because trumpet does have a few differences that are not related to the above mentioned musicians. For instance the sax does have a REAL octave key.
The tuba in its upper register only needs 1/8 th the pressure that a trumpet player needs to play a high c. And our notes do go up from there. (Ever see a tuba player pass out while playing? NO a trumpet player should NOT pass out but it does happen.) In theory it does work in the same way so clearly a tuba player could teach air usage. However I think that a trumpet player would understand our needs and requirements more fully.
As for air curing embouchure problems it is true that some problems can be taken care of by learning how to breathe and use the air. In fact it may be that 50% of all trumpet embouchure problems are related to a poor use of air. It may be that all tuba problems can be fixed by air usage. There is 5 times the room for error in regard to mouthpiece placement. And while it is easy to pin down the lips with a trumpet mouthpiece the same is not true of a tuba mouthpiece.
I’ve mentioned several times on the net about my first lesson with Jacoby. It was ALL breathing and air usage. That first lesson WAS the most important trumpet playing lesson of my life.