Software is protected by copyright. Some software may also be protected by patents, but last time I checked, AI generated output of any kind was not patentable.
Also, if model output distillation is shown as some form of reverse engineering I assume the DMCA can apply
I agree that you can't patent a book, but I would point out that you can patent an idea, which may only appear in a book or journal article.
Who are you saying owns that IP? The people who trained the model? The people who ran the model? The people who wrote the prompt? The person who paid for all of that to happen?
If the model output is owned by the person prompting it and paying for the tokens, what's the problem here?
If the model output is owned by the trainer of the model, that's a big nasty can of worms.