I don’t think I’ve ever come across a truly convex mouth before. But I’ve certainly tried my fair share of bowl and v-cup mouthpieces.
I know most people find that concave (bowl) shaped cups afford a brighter easer upper register, but for me I’ve always found V-cups better.
While the sound might not be as naturally bright, there’s a trade off – the v-cup seems to allow for more volume (loudness) which lights up the horn anyway.
I’ve always wondered about convex. I imagine those would have a similar quality to the v-cup in channelling the air more.