The bore size of a trumpet is pretty much insignificant as a single parameter. There are bright and dark small and large bore trumpets, there are free blowing large and small bore trumpets. The achievable volume is not a function of the bore, rather the efficiency of the working system. We are not listening to an amplified buzz of the lips, rather a resonance (standing wave) in the horn. Due to a mismatch in the length of the horn and the bell shape, a small portion of that resonance “leaks” out. That is what we hear.
It is safe to say that most trumpet building companies do not have a specific sound color that they are building. They may have - by luck, found something that works and is saleable. Contrast this to the high end automobile industry where the sound of an exhaust system, slamming door, road noise leaking into the passenger area are all carefully engineered.
What is the common denominator of Schilke trumpets? I would say manufacturing quality, not a tonal characteristic. Bach is known for their core - something that has not changed or improved for decades. Yamaha on the other hand reinvented the trumpet sound with a Xeno. There is a characteristic tone through the whole range of those trumpets. The better Bachs from many companies also offer no real tonal advantage and those companies building them did not have tone as the goal, rather only sales.
In my world, next to Yamaha is Monette. He is not the Burger King of trumpets, you don’t get it your way. The trumpets have a characteristic sound that is consistent through ALL of the models.
There is plenty of room for innovation. We simply need to start asking the right questions and that starts maybe 50 feet in front of the horn. My first question would be “do trumpets need to be as loud as they are”. I believe that most modern trumpets have a dramatically comprimised tonal palette of colors due to the fact that they were built for louder. The first lawsuits have been won because of the damage that the brass intensity causes in orchestras. Can’t we get that glorious halo around the sound at a lower loudness? Most certainly - but not from companies selling bore size.
Many want simple answers to complex questions. That is normally a sign of something not good ahead. That is how politics work and we all know how that ends up.