Now, in theory, you learning from an author's works and competing with them in the same market could meaningfully deprive them of income, but it's a very difficult argument to prove.
On the other hand, with AI companies it's an easier argument to make. If Anthropic trained on all of your books (which is somewhat likely if you're a fairly popular author) and you saw a substantial loss of income after the release of one of their better models (presumably because people are just using the LLM to write their own stories rather than buy your stuff), then it's a little bit easier to connect the dots. A company used your works to build a machine that competes with you, which arguably violates the fair use principle.
Gets to the very principle of copyright, which is that you shouldn't have to compete against "yourself" because someone copied you.
This is one of those mental gymnastics exercises that makes copyright law so obtuse and effectively unenforceable.
As an alternative, imagine a scriptwriter buys a textbook on orbital mechanics, while writing Gravity (2013). A large number of people watch the finished film, and learn something about orbital mechanics, therefore not needing the textbook anymore, causing a loss of revenue for the textbook author. Should the author be entitled to a percentage of Gravity's profit?
We'd be better off abolishing everything related to copyright and IP law alltogether. These laws might've made sense back in the days of the printing press but they're just nonsensical nowadays.
I think, in your example, the obvious answer is no, they're not entitled to any profits of Gravity. How could you possibly prove Gravity has anything to do with someone reading, or not reading, a textbook? You can't.
However, AI participates in the exact same markets it trains from. That's obviously very different. It is INTENDED to DIRECTLY replace the things it trains on.
Meaning, not only does an LLM output directly replace the textbook it was trained on, but that behavior is the sole commercial goal of the company. That's why they're doing it, and that's the only reason they're doing it.