It seems you are quite correct, when you write a 45 caliber wound channel is plenty large to cause hurt, and damage to living tissue. It is seemingly obvious that a bullet this size would be plenty large enough to put a deer down. However, there is another factor at play when using bullets that expand, besides the diameter, and the size of the hole made.

One way to view the changing of the shape of a bullet, or making it a larger diameter, is to picture that a force is required to do this work. This force comes from the lung, heart, etc. tissue. If the bullet didn't expand, the tissue wouldn't have to exert this force. It is the exerting of this force on the bullet, to make it expand, that leads to much more damage of tissue, than there would be, if the bullet retained it's shape, and punched a 45 caliber hole. Right or wrong, the view that it is the tissue that does the work to change the shape of the bullet, explains to me, why expanding bullets are more better.