I don't consider domesticated cats to be natural predators.
Natural predator populations rise and fall with prey populations. We humans supplement the cats diet (and birds for that matter).
- but there is a documented decline in songbird population, so I think the cats have the advantage.
Cat ownership has never been higher.
There's no dispute that cats naturally hunt birds - it's not like we train them to do something unnatural to the species. A better argument is that domestic cats aren't subject to the same threat of being hunted and eaten themselves, therefore the cat population is higher than it would be if the playing field was level. So in that sense we would agree.
By the way - I'm not a cat person so I definitely don't contribute to the cat problem. We do however have a Jack Russell who considers himself a bird hunter. Luckily for the birds, he's not that good at it!