Bumping the air button is important. If one does it correcty (slight and proper, depending on where the bellows are when player is when playing, both in the respect of pushing and pulling), tight/new bellows will work to your advantage.
Be happy when your bellows have broken in naturally, by this time you will be a pretty good accordion player, if you've listened, watched and learned from the masters.
please understand that when you push the air regulator, you must not hold it in. Perhaps if you feel that on quick push/pull situations you must hold it, this may work for you. Don't hold it in too long and volume will not be sacrificed. Think of the regulator as a tiny breath that the accordion must take in order to keep from dragging out too far. This will keep you pulling out only a few inches. That is, if the compression is correct in the accordion (if your leather's are curling inside, then you have a problem)
Handmade accordions from Louisana mostly don't require one to man-handle them in order to get volume, even with the slight palm-tapping of the air regulator
__. Yes, understand and agree with everything you say. And, somewhat slightly in the same vein, Sabin Jacque (a dynamite Quebec player) teaches to start a note with the air button slightly depressed and them letting it up smartly. The resulting "bump" of pressure will make a reed sound more quickly than you can do otherwise. (Of course, this is an effect that must be used very infrequently but it's great when you need it.)