Human beings, other than those who were native to this continent, also do not belong in this eco-system. As predators, we have killed, eliminated, and toppled over the natural eco-system since we landed on this soil. We have helped to bring many different species close to the brink of extinction, and wiped out natural predators for the past 400+ years. And let's face it: cats don't come even close to wiping out any species faster than mankind has done.
Any bio-system needs a food chain in order to keep that fragile balance going, and there is really little here that we haven't completely put out of whack.
While cats are not native to the Americas, they came on the same boats with the Europeans who came here, and likely helped keep those people alive in the first place--ships at that time employed cats to keep the mice and rat pestilence down and keep the grains safe. Personally, I would prefer to have the cats around than disease-ridden vermin.
In addition, the population of birds globally has declined, not from feline intervention, but from human beings and loss of habitat. In fact, overall, human beings are indeed the worst predators on the planet.
Wiki says:
Bird conservation is a field in the science of conservation biology related to threatened birds. Humans have had a profound effect on many bird species. Over one hundred species have gone extinct in historical times, although the most dramatic human-caused extinctions occurred in the Pacific Ocean as humans colonised the islands of Melanesia, Polynesia and Micronesia, during which an estimated 750-1800 species of bird went extinct.<1> According to Worldwatch Institute, many bird populations are currently declining worldwide, with 1,200 species facing extinction in the next century.<2> The biggest cited reason surrounds habitat loss.<3> Other threats include overhunting, accidental mortality due to structural collisions, long-line fishing bycatch, pollution, competition and predation by nonnative invasive species,<4> oil spills and pesticide use and climate change. Governments, along with numerous conservation charities, work to protect birds in various ways, including legislation, preserving and restoring bird habitat, and establishing captive populations for reintroductions.
Cats have been associated with mankind for over 9,500 years, and will likely follow us into space when we finally have the technology to go there--I have no fear that there will be vermin for them to catch even in outer space.
People who don't like cats are determined to make them the world's greatest enemy. But cats have been, and always will be, our companion animals as much as any dogs, rabbits and other small animals are. And they earn their keep in many places where some pets don't even come close.
Feral or not, cats are hardly the dreaded hunters that some make them out to be--for every "kill" of a bird, there are thousands, if not many more, diseased rats, mice, voles, and other pests killed in the process. In fact, many birds themselves carry diseases, an uncomfortable truth in the present with West Nile.