The numbers they have to kill to be a problem are not billions, but hundreds. Some years back, the European Turtle Dove was estimated to only have 135 breedable

The numbers they have to kill to be a problem are not billions, but hundreds. Some years back, the European Turtle Dove was estimated to only have 135 breedable pairs left in the entire country of Denmark - the approximately one million house cats in Denmark would only have to kill just 135 birds to make that one go locally extinct at that time. Four billion birds isn't a lot globally, but cats aren't hunting geese or swans - the number to compare to is the number of prey-sized birds in a local area where they can be hunted by outdoor or feral cats to notable population drops or local extinction. You might just see "a bird" or "a dove", unaware that it's one of several dove types native to your area with few remaining individuals. Cats are particularly effective/aggressive predators in that they hunt and kill for fun, without interest in eating the catch. This makes their impact much greater than it needed to be. Now, you can then argue against that conservation is necessary - animals outcompeting each other to complete extinction is normal, and we also hypocritically domesticate animals and take them out of their natural habitats - but it is something we generally aim for by protecting species in decline, actively controlling and fighting invading species, and attempts to reintroduce locally extinct species, and we tend to use any deviation from the status quo as a measure for environmental health.