Due to the trajectory and power it would be sensible to limit the distance to less than 50 m. A reasonably good marksman should be able to achieve a hit in the brain or upper spine at this distance. Around here fallow deer is kept as livestock. Those deer are frequently killed with shots from .22 lr or .22 magnum to avoid damage to the meat.
A bigger round like .222 is very likely to scatter small animals like birds or rabbits over a pretty big area. This will not leave much to eat. Small animals are easier to find and take in most areas. So it may be smarter to go for the smaller round in a survival gun. Anything too big is likely to be left at home. Using the .22 for hunting bigger game means going to if not over the limit of that round. So I would not advocate this for regular hunting.