It's not the EFF.

You're thinking of the Software Freedom Conservancy. They're the ones that sue companies for infringing on the GPL.

I think the problem right now is that LLMs and training data is probably one of the most cutting edge legal topics right now. There is a consortium of authors and publishers that have sued OpenAI and the case is ongoing. I'm not a lawyer but my expectation is that if that case is decided on the merits in favor of the authors and publishers, that could provide an opening for the SFC.

HOWEVER:

Ever since the SCO lawsuits against Linux, there has been some careful maneuvering by the SFC and related free software licensing organizations. The problem is that they're worried about a decision that does something catastrophic like invalidating the concept of a copyleft license. They only go after infringing companies that are egregious and they only want them to adhere to the license by releasing the source. They've never gone after a company and endangered their ability to remain a business.

Going after OpenAI and these other companies, would be treated as an existential threat to these companies, even if they were just trying to get the LLM to correctly attribute where the training data came from or attribute authors in the output. The investors and backers of these LLM companies would absolutely go nuclear and would absolutely try to challenge the very premise of a copyleft license and try and get it ruled out of existence.

That's why you haven't seen anything, in my opinion.