During the depression, my dad kept venison on the table for his widowed mother, with a single shot 22 rifle. Many times they couldn't afford to buy long rifles so they made due with shorts and longs. He just got close and shot them in the head. These were mule deer, not those easy to kill whitetails.
That being said, any legal hunting round that you can consistently score in the high 30s with at silhouette, should be a good hunting round. Do I do it? I haven't because I own a 30-30 barrel and a 357 max barrel and with them I don't have to go for a head shot, but if I didn't have those two barrels, I would use the 22 hornet barrel that I use for Hunters Pistol. From a rest, which I always use when deer hunting, I could be confident of a head shot out to 100 meters. A 22 hornet is legal in Idaho, by the way.
I know a guy out in Parma that elk hunts with a 22/250. He gets a big bull each year with it. His method is to set up on a high outcropping and glass. He tries to shoot at least 400 yards but prefers 600 yards. He places his shot just behind the shoulder. He is so far away that the bull doesn't know it is hit. It just flinches and keeps on grazing. A few minutes after the shot, mister elk would go down. I don't try this, I use a 338 win mag for my elk.
Sixgun