I never treated all or any birds at bird feeders as invasive. I said that they have no predators because we killed them all. I haven’t seen any data on how many birds a cat can kill vs an owl…I suspect an owl is more effective. I haven’t seen any data that suggests that cats are threatening any bird populations.
It just sounds like something that need to be managed…and we should consider something other than the cute birds we want at bird feeders.
Humans brought rodents, and killed their predators. Are cats killing more rats and mice than a weasel could? Unlikely.
Some edge case about a cat wiping out a bird population on an island 100 years ago doesn’t interest me.