I think you are somewhat wrong. I suppose in the city or suburbia you might have a point, but for those of us rural landowners, loose dogs often pack and kill farm animals. I can’t tell you how many chickens I’ve had killed by someone else’s dogs.
My neighbor has about 45 head of angus. They’re starting to drop calves now, but the first calf was killed by a pack of crossed pit bulls, Labradors, coon hounds and chows. He killed three of them. Sad that some of them had owners who let them loose outside and didn’t think that was a problem. I’ve shot at these dogs before just to keep them off my property.
Since we have maybe 1 sheriff’s deputy per every 100 square miles down here, calling the police doesn’t cut it, they advise us to shoot nuisance dogs.
In your situation it’s no different from killing a wolf. Mad dogs are in the same category. I’m talking about a cop who shoots a puppy.