Meet Gareth Morgan, an economist from New Zealand. He is concerned about his country's bird population. New Zealand has a large number of bird species endemic to the region, but many if not most are under some sort of threat. Therefore, the birds' predators need to be watched carefully.
Cats eat birds. So the solution, to Morgan, is quite clear: rid New Zealand of cats. Leading with the phrase "That little ball of fluff you own is a natural born killer", he has created the website Cats To Go, centered around the goal of getting cat owners to kick the habit, opting out of replacing their cats when they die.
When articles about your hopes and dreams can be countered with stock images of cute kittens, such as here, or here, or perhaps here, you really ought to reconsider your odds. The poll Morgan has attached asking people of they'll opt out of replacing their cat when it dies is showing a roughly 80-20 split in favor of 'no'. Cat owners have savaged him for insulting members of the family. The New Zealand SPCA has savaged him for rather obvious reasons. The statistics have savaged him, saying the cats are more interested in killing rodents than killing birds and their removal would create a host of new problems to the ecosystem.
And New Zealand is a particularly hostile nation for something like this. 48% of New Zealand households own a cat. By comparison, 33% of American households do, including mine.
There is an issue with feral cats- which do sometimes kill wildlife- but the solution provided by animal groups is basically the same one you already know: get the feral cats off the street, find homes for all the cats you can, help control the pet population, have your pets spayed or neutered.
So, yeah, go do that.