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Having done dissection on well over a hundred game animals from over 40 years of hunting gives me an excellent basis for evaluation of terminal bullet efficiency.
Your one size fits all theory just doesn't work. One of the main factors that your hypothesis failed to entertain or comprehend is bullet construction. Choosing the proper bullet to preform at the desired velocity for the selected animals density is important. When you discard all loads for all high powered rifles at 100 yards you are completely disregarding the fact that there are many bullets that are specifically designed to excel on deer sized game at that distance at higher velocities. When you lump all of the bigger rifles and the tens of thousands of loads all together you are demonstrating a whole bunch of what you don't know.
I shoot a wildcat round while hunting. It will accurately put a 170 gr bullet out of the muzzle at 3K fps with a 100 yard velocity of about 2850 fps, and a 200 yard velocity of more than 2500 fps. The bullets that I load for deer are specifically designed to expand and mushroom at 2500-3000 fps within the first inch of penetration. This means that the bullet I load for deer will preform on the game as it is intended to do from the muzzle of that rifle out to 200 yards. When hunting elk, moose, bear or any of the bigger game animals I shoot the same weight bullet at the same velocity but this is a different bullet that is constructed with a thicker copper jacket that will provide far greater penetration before it begins to expand. I want the bullets to properly expand and expel all of their energy into the animal. The perfect bullet choice is the one that sheds all of it's accumulated energy into the animal, mushrooms to at least 2X it's original diameter, and stops just under the hide on the off side. When you shoot through an animal all the energy after the bullet leaves the animal is wasted. Lets go back to your 44 mag. You said nothing about bullet choice. The bullets that have the best energy displacement at 25 yards are not going to be the best choice for that 100 yard shot. Those bullets too have a velocity window where they are made to preform. I don't know what bullet you are shooting but you need to know how that bullet was designed to preform and at what point in the decreasing ark of velocity this performance begins to degrade. There is one more term you need to become familiar with. Ballistic coefficient. That is the combination of all the math on bullet shape, aerodynamics, velocity, bullet weight and a few other things that determine the physics of how well a given bullet retains energy downrange. A pointed or semi pointed boat-tail bullet around .284"/7MM diameter retains the largest % of energy downrange. The wider blunt nosed bullets like the 44 mag shoots shed energy the fastest in flight. Have a nice day.

Your one size fits all theory just doesn't work.

What doesn't work is thinking anybody could manufacture a bullet which would expand properly both at 50 and at 300 yards. The 44-45 caliber bullet doesn't HAVE to expand. A common experience outfitters have is for one hunter to shoot a large boar with a 45 and drop him right there and the next guy shoot a boar the same size or smaller with a 300mag of some sort i.e. a rifle with two or three times the muzzle energy of the 44mag or 45LC and find the boar 150 - 300 yards off in the next field.

This is basically America's most lethal gun:

Inexpensive (around 530 USD on gunbroker all day long), accurate, and powerful. Chambered for 45/70 and using Garrett ammo it kills African game more efficiently than all but one or two of the largest magnums. In 45LC or 44Mag it will drop any American game at the normal <=100 range at which 90% of game animals are killed, and holds ten shots. It's arguably your best normal hunting rifle.