Actually, many hunters DO use hanguns (including my own brother, who uses, during the appropriate season, a .44 Magnum revolver with a 10" barrel). I have gone hunting for squirrels with a .22 semiautomatic pistol (didn't get any, didn't even fire a shot). And were I to go into the woods around here I'd carry my .38 Special revolver (although not for hunting -- the cougars here HAVE been known to attack people) and I'd prefer a .357.

But between heavy stuff suitable to hunting deer, etc. and small stuff useful for squirrels and rabbits, I can't figure out what the middle range would be useful for in hunting.