"Finish shots" with a handgun can land you in an awful lot of trouble. Unless it is a legal weapon to hunt with, you would have technically taken the game illegally.
I carry in the mountains because of the coyotes, bears, wolves, mountain lions, etc. Standard defense is another reason guys carry up there. Believe it or not, I've run into some really sketchy people at 11,000 ft in wilderness areas.
Some guys also carry just in case they want to shoot around on a slow afternoon.