They literally do not pass the criteria. LLMs use the entirety of a copyrighted work for their training, which fails the "amount and substantiality" factor. By their very nature, LLMs would significantly devalue the work of every artist, author, journalist, and publishing organization, on an industry-wide scale, which fails the "Effect upon work's value" factor.
Those two alone would be enough for any sane judge to rule that training LLMs would not qualify as fair use, but then you also have OpenAI and other commercial AI companies offering the use of these models for commercial, for-profit purposes, which also fails the "Purpose and character of the use" factor. You could maybe argue that training LLMs is transformative, but the commercial, widespread nature of this infringement would weigh heavily against that. So that's at least two, and arguably three out of four factors where it falls short.
FFS, the issue is not that the AI model "copies" the copyrighted works when it trains on them--I agree that after an AI model is trained, it does not meaningfully retain the copyrighted work. The problem is that the reproduction of the copyrighted work--i.e. downloading the work to the computer, and then using that reproduction as part of AI model training--is being done for a commercial purpose that infringes copyright.
If I went to DeviantArt and downloaded a random piece of art to my hard drive for my own personal enjoyment, that is a non-infringing reproduction. If I then took that same piece of art, and uploaded it to a service that prints it on a T-shirt, the act of uploading it to the T-shirt printing service's server would be infringing, since it is no longer being reproduced for personal enjoyment, but the unlawful reproduction of copyrighted material for commercial purpose. Similarly, if I downloaded a piece of art and used it to print my own T-shirts for sale, using all my own computers and equipment, that would also be infringing. This is straightforward, non-controversial copyright law.
The exact same logic applies to AI training. You can try to camouflage the infringement with flowery language like "mere extraction of relationships between components," but the purpose and intent behind AI companies reproducing copyrighted works via web scraping and downloading copyrighted data to their servers is to build and provide a commercial, for-profit service that is designed to replace the people whose work is being infringed. Full stop.