Most cats do tend to stay inside the house, or briefly go outside before coming back in again. Some animal-protection org here once published a story about the number of birds killed by cats which worked out to each cat in the country killing something like three birds a day, including all the cats who never go outdoors or who are way to comfortable to ever chase anything more mobile than a food bowl. After that I stopped paying attention to claims about bird numbers.

Not to mention that the cats who aren't too lazy to chase things are far more likely to go for ground-based animals like rats and mice than birds. As in, the rats that would be raiding bird nests if the cats didn't keep their numbers down.