I'm sorry if this is strawmanning you, but I feel you're basically saying it's in the public's interest to give more power to Intellectual Property law, which historically hasn't worked out so well for the public.
Copyright as far as I understand is focused on wholesale reproduction/distribution of works, rather than using material for generation of new works.
If something is available without contractual restriction it is available to all. Whether it's me reading a book, or a LLM reading a book, both could be considered the same.
Where the law might have something to say is around the output of said trained models, this might be interesting to see given the potential of small-scale outputs. i.e. If I output something to a small number of people, how does one detect/report that level of infringement. Does the `potential` of infringement start to matter.
Not necessarily. An alternative could be to say that all models trained on data which hasn't been explicitly licensed for AI-training should be made public.
The problem (as far as this specific discussion goes) is not that IP laws exist, but rather that they are only being applied in one direction.