As I see it, the biggest problem with cats is that they reproduce pretty prodigiously. I live in an urban environment and the feral cats are something of a neusance but I don't see many mice or rats which means I can keep my compost pile with impunity. If the cats are "fixed" (I prefer broken, but thats a different story) I think they do have a place.
When we lived in the country (rural East TN) we had lots of mice, voles, opossum and all manner of other creatures that can play havoc with crops and stored food. I was DEFINITELY thankful for the cats then.
In some way, I think the attitude toward cats (and sometimes dogs which are very useful in certain environments) is a lot like the attitude toward ornamental plants and invasive species. Bamboo is an "invasive" but it is also quite a useful building material. If you are homesteading and plan to stay and manage a stand of bamboo it is probably OK to keep a stand of it. Japanese maple aren't "useful" but they are beautiful and I think there is a place for beautiful organisms within reason (food for the soul). Dogs can protect your garden from rabbits and alert you to the presence of all sorts of unwelcomed guests (four leged AND two legged).
Its about context, management, careful integration and setting responsible limits.