There’s no law against “using” copyrighted works, there is a law against copying and distributing them.
Fair use analysis doesn’t come into play unless we’re dealing with clearly established copyright infringement. What LLMs do doesn’t clearly qualify as any of the behaviors reserved to copyright owners. For example, it certainly doesn’t “copy” the things it’s trained on by any legal definition.
Law works on precedent and analogy when there’s no clearly on-point statutes or case law. The most analogous situation to what transformer models do is a person learning from experience and creating their own work _influenced_ by what they’ve observed. That behavior is not copyright infringement by any stretch of the imagination. The fact that it’s done with a computer is not as important as people seem to think it is.