Well, sure, there are loads that died out before humans showed up. But of those that existed when we showed up, we have exterminated almost all of them.

> Of course if they had survived to even antiquity, yes, we’d probably have hunted them to extinction.

Often it wasn't even hunting. New Zealand's various giant ground parrots weren't THAT delicious. We introduced invasive species which did the extermination for us, in that case (and many/most bird-y cases, at least).