It should, but also that is significantly different from what an AI model is.

It would be more like a list of facts and information about the structure of another work, and facts and patterns about lots of other similar works; and that list of facts can easily be used to create other, very similar works, but also it can be used to create entirely new works that follow patters from the other works.

In as much as the model can be used to create infringing works -but is not one itself- makes this similar to other cases where a platform or tool can be used in infringing ways. In such cases, if the platform or tool is responsible for reasonable protections from such uses, then they aren't held liable themselves. Think Youtube DMCA, Facebook content moderation, or even Google Books search. I think this is likely the way this goes; there is just too strong a case (with precedent) that the model is fair use.

Not the OP, but yes it absolutely should. The idea you can legaly block someones creative expression because they are using elements of culture you have obtained a monopoly of is obscene.