It's become a bit clichéd to say it but I think it's different this time.
The kind of "piracy" you're talking about wasn't depriving the authors of anything because you could always make the argument you weren't going to pay for it anyway. If, on the other hand, you were making copies and charging people for them, you could definitely say you were depriving the legitimate authors of that revenue. AI companies are very much doing the latter, not the former.
The other part of it is it's not just copying. Previously, if I decided to make a copy of a work without paying, I'm only copying the work, not the author's whole writing style. Now the AI companies are depriving authors of revenue from works they haven't even made yet.
If they were able to create a model de novo then they could truly claim it hasn't just been lifted from existing culture.