Trumpet mouthpiece front view large - (Photo credit: Wikipedia)
What's interesting to me is that while some mouthpieces can tend to aid in the ease of producing faster air, that's all a high note really is. Players who turn to shallower cups tend to play with a brighter sound in general (hence the jazz mouthpiece). Once in a concert setting, they tend to return to a "C" cup or a "B" cup and regain a "classical" tone (hence the classical mouthpieces).
If a player learned to develop a clear upper register on a "C" cup, they wouldn't necessarily have to switch mouthpieces and confuse muscles, air stream, embouchure, or their minds with varying degrees of myths!
The mouthpiece that I've developed is close to a "C" depth, what I've changed for my playing is the rim size. I have found that the rim size affects my comfort - not my tone. There are other variables in the anatomy of a mouthpiece that will either enhance or hinder one's tone and range, such as backbore, throat size, etc. But if we stay with a standard backbore and throat, such as in the Bach line of mouthpieces, we can change tone just by changing cup depth.
This is what most trumpet players don't want to face up to - if we just did the work without looking for equipment to do it for us, we'd come out with a lot more money in our pockets and a lot less frustrated! My line of mouthpieces are great because they don't offer a bunch of hocus-pocus, empty promises, or claims that they will give you range that you don't already have... they do offer a more comfortable rim, and variable rim sizes in a kit form - something that most manufacturers don't do.