A derivative work that does not interfere with the commercial exploitation of the original is one of the major categories of fair use, even if the derivative work is commercially exploited. To run afoul of copyright, a substantial portion text needs to actually be reproduced.
Style cannot be protected by copyright—it is not a product; to litigate against human imitators, complainants need to prove there is some attempt to trade on an association with the original. For example, when Scarlett Johansson went after OpenAI for the Her-imitation voice, Skye, she was able to demonstrate that Sam Altman tweeted "her" and that she'd turned down an offer to supply her voice previously. Similarly, companies have gotten in trouble for hiring imitators to perform sound-alike songs in TV commercials when the original performers and songwriters turned them down.
In general, when an LLM produces something specific, it's because it was told to do so. ChatGPT will happily regurgitate Bible verses, for example. Only when there is a single clear way to respond to user input will you see obvious copying. The often-spouted misinformation that they're just blindly regurgitating things they've been fed previously is the result of not understanding the technology. Except in the case of fine-tune datasets being used for retrieval-augmented generation, the authors of training data have no more claim to the AI's output than the authors of the books you read have a claim to your own thoughts.
A human author writing "in the style of" (i.e. imitating) another author is still going to draw on their own experience and their own technique, even if it's subtle. And they still need to come up with an original story that will work with that style. That's why "style" can't be copyrighted - because human authors make what they write their own (IANAL).
LLM's absolutely do not and cannot. They have nothing else to draw on other than the original, copyrighted material. There is an input and an output, however complex the process in between. So whatever LLM's produce is necessarily derivative, unlike a human author writing an original story the way they imagine the other author might write it.
Also, for an LLM, the only way I can get something "in the style of" a particular author is to digitally copy their original works into the system. If those works are copyrighted, and I don't have permission to do that, that's infringement.
"A derivative work that does not interfere with the commercial exploitation of the original is one of the major categories of fair use"
If the market is flooded with cheap, AI-generated derivative work that is on par with the original author's work, and in the same genre, that would seem to be interfering with the commercial exploitation of the original by competing with it. And who knows if that author will get opportunities to publish new work if they're competing with an AI that is trained on their earlier work?
