The act of training the AI on the material may be fair use, but the unauthorized access is a different story. That's probably why the Writer's Guild lawsuit against OpenAI focuses on the downloading.
Most of the arguments I've seen around this bullshit is that the AI is just like a human so it should be able to train on anything it can see. I don't think many understand what you've touched on here, which is that all the content piracy for explicitly commercial purposes is the actual problem here, not the training of AI.
There would be no fines at all.