It isn't fair use, See most of faq @ fairuse faq.

"Fair Use" is often the subject of discussion when talking about online copyright with regards to online video content or music sampling, but it's notably a flawed defense as it generally has no legal definition for how much of certain content can be used or referenced. The very first line of that faq has the following note:

How do I get permission to use somebody else's work?
You can ask for it. If you know who the copyright owner is, you may contact the owner directly. If you are not certain about the ownership or have other related questions, you may wish to request that the Copyright Office conduct a search of its records or you may search yourself. See the next question for more details.

All artists / writers and others are asking LLM model producers to do is a) Ask for permission or B) Attribute the artists work in some kind of ledger, respecting the copyright of their work. Every work you make (write/play/draw/whatever) has a copyright that should be respected by companies and are not waived by EULA or TOS (ever) and must be respected in order for author attribution as a concept to work at all. There is plenty of free, permissive copyrighted content on the internet that can be used instead to train an LLM, but simply asking for permission or giving attribution would at least be a step in the right direction for these companies and for the industry as a whole.

Defenders of AI will note that the "use" of art in LLM is limited and thus protected by fair use, but that is debatable based on the content of the above listed FAQ.

How much of someone else's work can I use without getting permission?
Under the fair use doctrine of the U.S. copyright statute, it is permissible to use limited portions of a work including quotes, for purposes such as commentary, criticism, news reporting, and scholarly reports. There are no legal rules permitting the use of a specific number of words, a certain number of musical notes, or percentage of a work. Whether a particular use qualifies as fair use depends on all the circumstances. See, Fair Use Index, and Circular 21, Reproductions of Copyrighted Works by Educators and Librarians.

You can see that the use cases above (commentary, criticism, news reporting and scholarly reports) does not qualify LLM companies to use or train their models with copyrighted data for privatized industry. Additionally, you'll note that "market disruptive" uses cannot be protected by fair use in it's definition, meaning that displacing artists with AI automatically makes LLM use of copyrighted material an infraction of copyright that is not protected by the fair use clause.

Regardless, this will need to be proved in court and even if it passes certain criteria, it will not apply to all infractions. Fair use is a defense, not a protection, and thus LLM producers will have to spend time in court in order to defend individual infractions. There's no way for them to catch all copyright infringement with one ruling, it needs to be proved on a case-by-case basis.

IANAL but this is my 2 cents on the matter.