Cats usually won't tackle rats, this is even mentioned in the article.
Joking aside, cats aren't going to be very inclined to head into a lair to pick off their young.
For example, while cats might kill a lot of animals in settled areas like NYC that doesn't at all mean that species are endangered as a result of it. Birds don't exclusively live in human settlements and their continental populations might barely be affected by cats as there are sufficient areas outside of human settlements where feral cats are simply non-existent or at least not a problem.
Furthermore, the decline of birds is almost entirely human made - no one doubts this. Habitat loss and insect decline. Reducing the cat problem will simply not have a notable impact at all. Yes, millions of birds are killed by cats but what does that mean in the grand context if billions and billions of birds are killed by humans? It's a drop in the bucket and not worth the effort and I would ask ornithologists to name species that have been wiped out by wild cats in a continental context and not just from Smallstown, Minnesota.
Disclaimer: island scenarios like New Zealand are different due to the locality of the problem.
It's like trying to save ants from some dude stepping on their streets once a day while ignoring a ravaging fungus that is destroying the colony from the inside. But here you are, saying "not stepping on the ant street is also helpful!". Congrats to saving 10 ants while the colony is being decimated by a fungus.
I don't know of any "cat breeders". They are just a resilient species.
I suppose we could make some sort of "equity" system for species based on an arbitrary metric, but that's closer to playing God.
Birds can fly, not really fair to the feline species concerning which places it's allowed, eh?
Zero cats should be allowed to exist in NA?
No open borders for cats!?
Zero non neutered cat should be allowed to exist in North America, correct.
Same applies to humans of non-native descent, I presume?