I'll note that there are plenty of models out there that aren't LLMs and that are also being trained on large datasets gathered from public sources.
Image generation models, music generation models, etc.
Heck, it doesn't even need to be about generation. Music recognition and image recognition models can also be trained on the same sort of datasets, and arguably come with similar IP right questions.
It's definitely a broader topic than just LLMs, and attempting to enumerate exhaustively the flavors of AIs/models/whatever that should be part of this discussion is fairly futile given the fast evolving nature of the field.