The benefit that generative AI has is that, when claiming copyright infringement, you need to specify individual works that were infringed. It's not enough to say "this work is an amalgam of these other ten thousand works, and we can't really tell you how."
I could imagine if generative AI gives an identical, word-for-word match for an individual piece of source material it could be in trouble, but that's also the easiest type of thing to prevent from an AI company perspective.
The fact is that existing copyright law just can't really encompass the kinds of societal concerns we have around generative AI.