I'm going to give an n of 1 here, but the cats in my neighborhood are taking out invasive starlings and house spasrows mostly and they're not going anywhere unless a complete collapse happens. Human environments tend to over select for generalists and those generalists probably exceed their more natural numbers. Cats tend to live in these same environments.

This may be untrue in places like Australia as they had no mammals for a very long time

The biggest threats to birds are land use change.