Mountain lions really keep away from people, but sick or injured ones love to eat household pets and livestock. Rare but it happens. My small kids play outside about a million hours per year.
The bears in AZ really seem to be getting acclimated to the population. Lot's of examples including one in downtown Kingman last year.
The bigger problem in my opinion (and in my part of rural AZ) is idiots who drive out of town and dump their unwanted dogs. Not the dogs fault of course. Most are just hungry/thirsty and friendly. Some aren't. Groups of wild or semi wild dogs can be a problem for livestock and sometimes people, specially little kids. That kind of brings ammo capacity into play.
Sick coyotes are out there, I've had (the old 36 shot series) rabies shots to verify that.
All of those things are pretty rare. Use of a firearm in self defense is rare too but we walk in a prepared manner.
My rescued shepard mix doesn't let anything within 100 yards of the house without letting us know what's up. And she'd die before she'd let something hurt the little ones. You can't buy that kind of 24 hour security for a million bucks.