Oh no! So sorry.. your cat shouldn't have brought it in the house anyways. The bird was most likely trying to defend itself. Keep your cat in the house next time and shut the doors, you should be fine :)
Most people like outdoor cats. Yeah they hunt but if you live on an acreage its either you have a cat or you have mice. Plus, I'm pretty sure there's enough wildlife around I doubt a few cats will wipe it all out.
yes you could consider cats invasive, but the biggest thing I've seen my cats manage to kill is a rabbit, other than that it's all mice snakes birds and squirrels, and just as there are many fish in the sea there are many rodents in the woods my cats hunt.