A better solution would be for the owner to be fined and required to attend a class on responsible pet ownership, much like traffic school. The best solution would be for people to talk to each other, reasonably and rationally, gain an understanding, and solve the problem.
I don't like killing; I can't imagine being gleeful at the death of any animal, especially since it is the owner's fault, pure and simple. I dread the evening I'm out with Charlie and he shoots a coyote, even, but must admit I won't try to stop him as it becomes a choice between the coyote and the safety of Bimmer or the puppies. I've had to school myself to remember, too, that dogs are predators and as long as they are going to eat what they kill, or reduce the barn rat population (which they evidently recognize as vermin and don't eat - the coyotes have decimated the wild barn cat population around here) and don't kill just for the sport of it, I can accept that.
As for neighbor's dogs chasing our cows, well, our dogs don't let them. Charlie's fired off shots over some dogs' heads in the past, and was angry enough to shoot the dogs if they showed up again, since at the time he had dairy cows and they are extremely vulnerable to dogs in ways that beef cattle aren't, but he spoke to the owners, and although a couple of them didn't see the harm in their dogs chasing cows, they kept them up afterward.
I believe North Carolina has passed a very intelligent law requiring developers to leave a buffer zone between residential developments and agricultural property. This type of requirement could alleviate many situations before they get started.
So, Diggy, please put yourself in that dog's skin for a moment. . .
You're running and playing and chasing and having a great time. No one's taught you that you shouldn't be there; your master lets you do it and pays no attention to the other man who chases you, so it must be part of the game. It's fun, it's a wonderful day. Look, that man's come out to play again. If you bark, you'll get his attention and he'll play with you. More fun! Noise. Pain, Confusion. Can't move. Can't get home. Alone. Dark. . .
Maybe you lie there, panting with fear, you hear your name called, but no one looks for you. Then night comes, and the coyotes find you. . .
Kind of puts a different perspective on it, doesn't it. And please remember, I can speak to BOTH sides of this issue.