My bet is that copyright law has not caught up with massive machine learning models that partially encode the training data, and that there will still be cases to set legal precedent for machine learning models.
Note also that it's not just a concern for copyright, but also privacy. If the training data is private, but the model can "recite" (reproduce) some of the input given an appropriate query, then it's a matter of finding the right adversarial inputs to reconstruct some training data. There are many papers on this topic.
It is almost certainly the case that current IP law is very unsettled when it comes to machine learning models and mechanisms that encode a particular training set into the output or mechanism for input transformation. What should probably scare the shit out of people looking to commercialize this sort of ML is that the most readily available precedents for the courts to look at are from the music industry, and some of the outcomes have truly been wacky IMHO. The 'blurred lines' case is the one that should keep tech lawyers up at night, because if something like that gets applied to ML models the entire industry is in for a world of pain.
Note also that it's not just a concern for copyright, but also privacy. If the training data is private, but the model can "recite" (reproduce) some of the input given an appropriate query, then it's a matter of finding the right adversarial inputs to reconstruct some training data. There are many papers on this topic.