Let's approach this from the other side, what happens when I have too little air?
Ability to play loud and long decreases
Ability to play big and long decreases
The muscles have to work harder to keep the lips under more tension

What's wrong when I have too much?
I have to expel air if I haven't used it up by the end of a phrase - that takes time and is additional work
the changes in my body state with a BIG breath are pretty great, that also needs to be compensated for.

My take: forget the dogmatic BS. Learn both ways: Efficient small breaths and massive big ones as well as EVERYTHING in between. This is not a choice between heaven and hell, beautiful and ugly or intelligent and stupid. I believe the zealots always lose in the end, as well as missing most of the fun between gigs. I am not a weight lifter that has only one goal: ever heavier, I am a trumpet player that needs everything between silky smooth to flame throwers, sexy to poisoned arrows. Let's get off this athletic trip - that is something for the weak in character!