My neighbor has an outdoor cat. This cat kills at least one bird a day according to their kids (the cat brings the corpse to their porch). So I think you're tremendously mistaken about "not at any great rate."
Housecats are not native to most countries, and feral cat colonies are not healthy either (lots of disease). They are not part of "natures balance" and we're not eradicating them to extinction. That's just utter nonsense.
You are the owner of a domesticated species. Feral cats are part of natures food chain and natural balance. Without them there would be no stopping the rodent population.Not liking them being there doesn't make them invasive.
No, they're not. They're an invasive species brought to different locations around the world via human activity. The feral cats being discussed originated in the middle east and were brought to different continents by humans. North America's native cat species do not naturally target mice.
This is like saying the argentine black and white tegu is a natural part of the food chain in Florida. Please understand that humans bringing a species to a new location doesn't suddenly convert them to part of nature.
Cougars, wolves, coyotes. eagles, snakes (venomous and constrictors), hawks, and owls are natural predators of cats. Their populations have been decimated mostly by loss of habitat (same with birds). Peronnally I'd much rather be overrun by feral cats than rats any given day.
Housecats are not native to most countries, and feral cat colonies are not healthy either (lots of disease). They are not part of "natures balance" and we're not eradicating them to extinction. That's just utter nonsense.