Obviously, this is a philosophical discussion, so I'll expound on another angle:
Speed kills. The mammal body is comprised of approximately 60% water. The faster a projectile hits that body, the more violent the shockwave that is created. That shockwave creates massive tissue damage. Certainly, ballistics and bullet design play a role which gets complicated pretty quick. The deer is a relatively small animal, so penetration is not important like it is with bears, moose, etc. This is why the faster bullets (243, 260, 25-06, 7mag, etc) are such good whitetail calibers.
I learned this lesson shooting deer with 243. I used to use bullets designed for penetration, usually in 100 grains around 2,900 feet per second. I noticed that the bullet entered and exited so fast that there was very little bullet expansion. The wound channel was little more than 1/4" wide with an exit wound about the same size. This deer bled very little and ran at least 100 yards. Recovery was a problem. The wound was akin to shooting it with a field point on an arrow.
I switched to a smaller, faster ballistic tip or soft point that had rapid expansion, I prefer 80 grains in the 243 traveling upwards of 3,000 feet per second. Ever since, I have not had a deer run 20 yards and most drop to the ground.
What is happening is that heavy bullet zips right through and the tissue absorbs little of the energy. Most of the bullet energy is absorbed into the ground or tree behind the deer. That ballistic tip is expanding or exploding and 100% of that energy is absorbed into tissue. There is usually no exit. That shockwave destroys tissue about 5" instead of 1/4", and the spinal cord is usually destroyed.
Having said all of that, I still mostly shoot a 308 which is not terribly fast. I'm complicated.