Joe, I think we both understand the problems, and just come at it from different directions. I have killed pheasants at 50 yds with a lucky shot of #7 1/2 shot. A pellet or two hit the head and neck of the bird and dropped it. On the other hand, I have also killed pheasants further than that using #5 shot, and they drop like they were hit with an anvil.
For short range shooting, the only reason that the smaller shot works so well is because of the increase in pellet energy on target DUE TO more pellets in the pattern. You are correct. But you can get just as effective results using slightly fewer pellets, but of a larger size, because you only need ONE pellet to hit the game to kill it. If you look at the Lyman Shotshell Handbook, you will find that where One pellet of #5 shot delivers enough energy at 30 yards to kill your rabbit or pheasant, it takes Two #7 1/2 pellets on target to deliver similar energy at that yardage. We all have seen birds " Dusted " by light pellets at long yardage where other than a few feathers floating to the ground, the bird flies off, apparently unharmed.
I once hunted with 2 other men, and we were using #6, #5, and #4 shot in our guns respectively. A bird got up in standing corn in front of me, and I shot it with #6, but it was just veering to my left toward the guy next to me, so he shot it within a second with #5 shot. About the time the bird was hit hard with that shot, and flaired its wings, it was hit by a load of #4 shot because the guy on the far Left of me had gotten a bit ahead of us, and though it was coming into his safe Zone of Fire. Well, it was well hit and dead at about 35 yards with my load of #6. It was smashed with the #5 shot load, and heading to the ground. But when it was hit by those #4 pellets, it went slamming to the ground. If I recall, we made the #4 shot guy keep the bird. Then we had a long talk about keeping our line of march as we drove the fields, and respecting zones of fire. The only thing we learned from that experience was that all three of us were good enough shots to hit a flushing bird.