Our neighbors have been able to get rid of their pest control services because of our cat. She has rid the neighborhood of rats, then mice, and has started in on the scrub jays, raccoons, and squirrels. (Yes, raccoons.) I think cats are on par with other "wild" animals - cats live outdoors because they refuse to live indoors, not because their owners don't care about them. Our cat, for instance, if we try to contain her indoors, will just wait behind the front door until we come home, and the second the door is open, she streaks out into the yard. A cat that wants to be outdoors will find a way. (Our other cat sees the benefits of being an indoor cat, and doesn't go outside.) But in exchange for us feeding her, she kills ALL of the vermin in the neighborhood (well, not all - some of them, she brings home maimed for us to enjoy). I guess our neighbors could all pay the pest control guys that they had before, and lay out poisons in their yards that their dogs or kids could potentially get into... or they can put up with the occasional presence of a cat in their yard, and allow her to take care of the problem for free.
It's interesting that as a dog owner, you don't see that your dog could potentially cause problems for your neighbors (other than pooping on their lawns). For instance, our neighbors on all three sides have dogs. It's rare that they're not barking. When one barks, all the others bark. I suppose I could complain that my neighbors don't feel badly about this, and point out how annoying it is to listen to their dogs bark all the time. However, the dogs serve a purpose just as much as the cats do. They help keep our neighborhood safe from burglars and alert us to strangers walking by. In exchange for that service, yeah, I listen to them bark. It is what it is.