It isn't about making things deader, it's about using it because you have it. A .338-06 or Whelen is no where near a super sized cartridge, they're based off of a .30-06. Now recoil from both can be downright brutal depending on a lot of factors, but it can be as well out of smaller cartridges.

White tail deer aren't extremely hard to kill, but then again most animals aren't. A well placed bullet with adequate construction and enough penetration into vitals tends to work well regardless of animal size. I'm not a minimalist either, though I've killed white tail with .223 and 6- 222 RM rifles. I tend to hunt with the rifles I own, and sometimes that means that I use them on smaller game than I imagined I ever would.

Some places still require use of shotguns only, others only .35 caliber and up and funky length requirements, or a .35 Wheels in a single shot rifle with exposed hammer is the choice for primitive hunting seasons in some states. However, I can tell you most of the time someone uses a certain cartridge on an animal for hunting is because they one because they can, and two because owning something and not using it is boring. Using most modern rifle cartridges on white tail is overkill these days, when most die very easily to a patched round ball at subsonic speeds, or a or a pointy stick launched from a bow.