This is quite inaccurate. I've watched many a cat hunt outside of bird feeders to see them catch birds that are perfectly fine.Pesticides kill most of the birds who die early either from direct contact or from killing the insects the birds need for food. Cats kill the birds who are old, sick, or weak, often from the effects of pesticides. Most cats don't actually chase birds, they tend to specialize - small animals, snakes, lizards, fish, birds. (Birds of prey and coyotes also kill birds, as do people with guns and even air guns.) People like to keep saying that cats kill birds because it's easier to blame cats than people or corporations, particularly giant systems like agra-business. After all if people started really admitting how many birds pesticides kill, they might start questioning how many people pesticides kill and we wouldn't want to go there, would we?
You might also want to consider whether it's kinder to let an old or sick bird slowly starve to death or die quickly by a cat. Your world view will determine your answer to that.
There would have to be those other creatures in your area for a cat to hunt them.
Even on the farm, our barn cats brought home just as many birds as they did moles, rats and mice (no lizards here). It was to my grandmother's great dismay how many hummingbirds were murdered by our indoor outdoor house cat! She got rid of the feeder in the end.
I don't think it's an 'or' situation regarding wildlife. There's many campaigns, at least here regarding pesticides killing wildlife including birds (more of a problem with owls and rat poison). Not so many about cats killing wildlife though you can watch it happen.