Generative AI is based on "predicting" and generating the next token. Tune it one way and it will regurgitate its training data exactly. Tune it the other way and the words it comes up with are nonsense. Tune it just right and it comes up with something that seems creative.
The problem is that the training data is always in there somewhere. It can't generate something in the style of Shakespeare without containing Shakespeare as reference. That's probably fine for Shakespeare which is out of copyright, but if it contains say Stephen King's entire collected works, that's another issue.
If a human writer read all of Stephen King's books then tried to write in the style of King, that would be OK, but that's because a human can't memorize everything King has written word-for-word. When a human reads King, they don't build up a database of "probable next word frequency", instead they build heuristics having to do with how he approaches dialogue, how he reveals character, how he builds tension, etc. They may remember one especially memorable line or two, but the bits they remember, even if written down word-for-word would probably not be enough to be copyright infringing on their own.
I would bet that we've come too far to completely scrap generative AI. Too many billions have been invested, and the companies have too much political power. So, the question is whether there will be significant changes to copyright law. On one side of that fight will be the trillions of dollars behind the entertainment industry. On the other side of that fight will be the trillions of dollars behind the tech industry. Of course, individual artists will be trampled in the process.