“Brass mouthpieces are symmetrical, flat and round for a good reason.”
In fact there are a number of reasons. You can decide if they are good ones.
The original mouthpiece for the ancestor of the trumpet was probably the end of an animal horn with the tip cut off and the edges rounded. This produced a symmetrical, flat, round ring.
When modern manufacturers started making mouthpieces out of metal the machine they had available was a lathe. Lathes are very good for making a symmetrical flat and round ring, so it makes sense that the shape persisted.
Of course this was fortunate because we all know that our teeth are perfectly flat and our lips are symmetrical and round. More importantly, years of research trying variations from the traditional design have demonstrated that the very best shape for a brass mouthpiece is symmetrical, flat and round. Right?
Wrong.
Most brass mouthpieces, with the exception of a few historical examples that very different in design from the Wedge and did not catch on, are symmetrical, flat and round because they always have been that way. Until now.