You are talking from no experience or very little knowledge of hunting and actually killing anything but time.. I actually sense a certain amount of arrogance in your statement as if you were the GREAT HUNTER and there is no one else capable or has the ability to kill any animal with a .22 other than a squirrel. We are not actually over run with Elk or Brown Bears or even Moose in GA if you haven't realized it since they are included on your list of animals we could not kill for food with a .22...I worked as a Game Warden, the caliber of choice by the majority of poachers I encountered is a .22LR. More big game animals are poached with a .22LR using head shots(shooting at animals at night in a light) than much more powerful, LOUDER calibers. A rifleman with adequate shooting ability can make head shots on calm( not alerted or running) big game all day long. You don't need any large caliber gun to get food if you are not some nimrod that point shoots and does a mag dump at everything.
I also grew up on a farm, we raised and butchered our own meat. We always used a .22 LR to put any animal down for butchering.. including twelve hundred pound steers...did it for more than twenty years and not one animal came back to life.....ever. When I was a kid, I shot a lot of Partridge, Turkey, Geese and other game birds with a .22 using head shots when ever the shot presented itself at a standing or roosted bird. It was perfectly legal way back then and more people hunted for food than sport. Depends on where you grew up and when I guess. The more urban people hunted their food at a supermarket where someone else did the work for them. I have seen Black Bear killed with a .22 LR with a shot into the ear cavity many times. In the 40's, 50's and early 60's Bear were considered a varmint and there was no season or limit on them in Vermont and Upstate NY. the way most hunters hunted bear was to use hounds and either bay them on the ground or hope they treed or hunted over bait, usually a dump or gut piles of other game killed and a head shot was relatively easy since there were no TV cameras around trying to make it a dramatic scene for the inexperienced hunters to be impressed with. To make a statement that the animals you listed could not be killed with a .22 LR actually shows how little experience you have on the subject.
I'm with this guy! The .22LR is soooooooooooooooooooooooooooo underestimated.