Let's assume model output can be claimed by copyright or some form IP. You can't really patent it, as the output isn't a novel idea or process, much like you don't patent a book or a movie. But for arguments sake, let's agree it is some kind of IP.
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.