IMO the focus should have always been on the potential for AI to produce copyright-violating output, not on the method of training.

If you try to sell "the new adventures of Doctor Strange, Jonathan Strange and Magic Man." existing copyright laws are sufficient and will stop it. Really, training should be regulated by the same laws as reading. If they can get the material through legitimate means it should be fine, but pulling data that is not freely accessible should be theft, as it is already.