I’ve had cats all my life, and never did one bring home a bird. They brought home mice and bugs.
But I’ve seen many eggs and baby birds - even pigeons and mourning doves - killed by crows; you see it daily in the Spring. And yet crows are still protected in this country - you can’t take one as a pet, even though in the past they were considered pests and dynamited by the roost-full.
My last one nailed three squirrels in one day and laid them on the patio for me, shoulder to shoulder in a neat row. To him, I'm a big, hairless cat that sucks at being a cat, and he doesn't want me to starve.
Miss him a lot, he was a terrific friend.
There is no shortage of ravens, fish crows and American crows that I can see. The so-called “protected” status is merely for the purposes of government control.
I had a 16-year-old one-eyed cat who died earlier this year. Up until fall of last year, he was catching and eating small birds, usually juncos but sometimes chipping sparrows (all adults), as well as mice and voles.