Maybe because we can't explain well what we do with our embouchure, with the air, etc.
We use to say "use lots of air". Yes. It can't be wrong. but when I did this it gave me a great headache. Because I was doing a tremendous pressure. Less pressure? No. pressure is needed up there. but how to do an efficient pressure, without blocking the air? (that caused me the headache)
Well, I have two wellknown tricks:
lower the embouchure in the mouthpiece (more upper lip, less lower lip causes lower lip to be smaller inside the mothpiece) and turn the lower lip over the lower theeth (this will make 2 things: the lower lip will get harder and the upper lip wil be touching a harder tissue on the lower lip)
these things helped me a lot. I gained an octave in the upper range. No headaches, no unesserary pressure.
The only problem is: I have to work on not moving my embouchure too much, or I loose flexebility on jumps.
Hope this helps.
Back to topic
I think it is possible that training with a big mouthpiece can help, possibly, to build a strong embouchure.
However if I have my favourite mouthpiece already, I would use it always. but that is just an opinion.
or if you are going to use a bigger one for training, perhaps you will get to like it and stick with it...
Training soccer with a beach ball will help your soccer?
Maybe...
