Hi Sage and all,
in line with what many have pointed out, I'd say it always depends.
From an ecological perspective, the main issue would be that cats also eat other creatures that have an important function in the balance of the system (a managed ecosystem, connected to unmanaged ecosystems neighbouring it).
Question would be, can our system support that level predator (has it reached a point through the plant natural sucession to create the appropriate habitat / niche for such a predator) ? If not or unknown, can you limit the acess of the cat to the ecologically most sensitive areas?
FOr instance, I have a wild boar AND mice problem right now. The neighbours cats are no longer coming to the land because we have had to install electric fencing to keep the boars out. I know there are falcons, owls, ravens and snakes around that can eat the mice (just seen a raven catch one), but likely not as efficient as a cat in controlling the mice population. However the cats where also eating the geckos, that help keep the balance in the agroforestry gardens.
The bottom line for me is to have the principles in mind, and be aware of the consequences and try to find a solution for the specific set of circunstances, that maintains coherence with those principles.
I love cats too
Hope this is useful.
Cheers!