First of all, fair use is not simple or as clear-cut a concept that can be applied uniformly to all cases than you make it out to be. It’s flexible and context-dependent on careful analysis of four factors: the purpose and character of the use, the nature of the copyrighted work, the amount and substantiality of the portion used, and the effect of the use upon the potential market. No one factor is more important than the others, and it is possible to have a fair use defense even if you do not meet all the criteria of fair use.
Generative models create new and original works based on their weights, such as poems, stories, code, essays, songs, images, video, celebrity parodies, and more. These works may have their own artistic merit and value, and may be considered transformative uses that add new expression or meaning to the original works. Allowing people to generate text that they would otherwise pay writers to create that isn’t making the original redundant nor isn’t reproducing the original is likely fair use. Stopping people from cheaply producing non-infringing text doesn’t seem like something the courts would agree should be stopped just 'cause someone wants to get paid instead.
I think you’re being too narrow and rigid with your interpretation of fair use, and I don’t think you understand the doctrine that well.