I’m at a friend’s place and the cat keeps bringing in dead (or half-dead) animals into the house. It’s my understanding that cats think we are big, helpless kittens that don’t know how to hunt. Hence, they think they are doing us a favour.
It seems like a few mice actually escaped and found refuge in some walls in the house, so these “presents” are actually more than just annoying (and smelly if the dead animal ends up behind the couch).
That’s the reason wildcats are not a problem, they have small stable populations and barely interact with humans and domestic cats.
“Modern” Wildcats have been in all of Europe for at least 300k years, so they were just another predator species among many others.