Another perspective:
Think of a 2-way HiFi loudspeaker with a large chassis for the lower frequencies and a small one for the higher frequencies. The large one takes 50 Watt, the small one 3 Watt. The bass frequencies draw the energy, that is why old-fashioned HiFi amplifiers had huge condensers. 100 Hz move a lot more air than 4000 Hz, bass peakers have a large membrane.
Let´s say the amount of energy that you can put into your horn shall be fix. Then you need much less of it to generate volume in the higher frequency range than in the lower one.
So when a mouthpiece has a large baffle, you can play loud easily = you have a lot of higher partials where you do not need a lot of energy.
With a lower baffle and less high partials, you need more energy to play loud, "blow harder", "proper breath support", ...
I am switching from a Berg Larsen type MPC to some Dukoff/Florida style type MPC now. And that is just what I sense, I need to put more energy in it to remain loud. This work pays off by a fuller, rounder tone, meaning less higher partials. Indeed, my Rock combo complained about me playing so loud (no mic), and they immediately noticed when I changed the MPC. I can still push, but what I get now is sound, not paint peeling off the wall...
Thinking about it, it´s loudness what I talk about. Well, that´s how I perceive the volume thing.