Yep, I live at the end of a country road. A lot of neighborhood dogs that get loose just walk down the road and end up at my place. Obviously, everyone is going to have a different experience, but I probably get a dozen loose dogs here every year and I can't think of a single instance where I would have considered it necessary to shoot them. The ones that aren't sociable enough to let me check their collars usually just run off scared.
That's not to say I wouldn't be upset with the dogs for killing my livestock, but I agree with the general sentiment that the responsibility lies on the owners. My family had a horse that was chased into a barbed wire fence by a group of dogs when we first moved out here. Even after it happened these people continued to let their dogs chase our animals, but my father refused to shoot the dogs just because the people were irresponsible druggies. Shooting the dogs wouldn't have stopped any of the stress my family went through with them as neighbors.
Years later my father actually put down one of our dogs after it got loose and killed a bunch of cats, and that was one of the few times I ever saw him cry/visibly shaken. He was a big, tough guy that worked the county jail too, so rare moments like that always stuck with me.
A dog would have to be pretty aggressive for me to consider shooting it.