From a kid, my trumpet teachers always stressed putting your right thumb between 1st and second valve. That always seemed awkward to me -just didn't feel correct. I always had a tendency to slide the right thumb to the front of the 1st valve. Bet some of you do too! And, if it was such an incorrect grip, then how are you supposed to operate a first valve trigger or thumb saddle, rig without holding it this way? (Just an interesting tid bit -walked into a shop of an 80+ year old fairly well known pro about a year ago and he immediately told me to hold the horn the right (classical grip) way.
Today, I was trying out my 1924 Holton -which is a longer horn that all my others and the distance from the leadpipe to to the other slides is also much more narrow or tighter. My guess is this is what some of you call a peashooter (not sure). At any rate, because of the narrow amount of room between the leadpipe and lower slide, there is no room for a thumb in front of the ist valve. Your thumb is forced between the first and second valve -as I was told to do during my early years of training. And, the longer bell etc. seems to positively effect the grip so the horn is balanced.
So is this the reason for the classical grip -peashooters? With today's horns offering much more room, many players seem to be moving to the thumb around the first valve.