This isn't just a matter of law, but of technology. Part of the point of these large language models is the massive corpus of raw data. It's not supposed to mimic a specific person or work, but rather imitate ALL of them. Ideally, you wouldn't even be able to pinpoint anyone or anything in particular.
(If you're asking about a different type of AI, then disregard)
Likeness is just one aspect of copyright. Another side entirely involves the protection of the innovative and production parts of the creation of the original training material. I.e. ChatGPT wouldn't be possible without the work of hundreds of millions of writers writing things.
Not so different than compensating a course for providing you with their learning materials when you learn a new language.