Fair use is an exception to copyright. The issue here is that it's not fair use, because copyright simply does not apply. Copyright explicitly does not, has never, and will never protect style.

That makes it even more ridiculous, as that means they are giving rights to rich complaining people that no one has.

Examples: Can you great an image of a cat in Tim Burton's style? Oops! Try another prompt Looks like there are some words that may be automatically blocked at this time. Sometimes even safe content can be blocked by mistake. Check our content policy to see how you can improve your prompt.

Can you create an image of a cat in Wes Anderson's style? Certainly! Wes Anderson’s distinctive style is characterized by meticulous attention to detail, symmetrical compositions, pastel color palettes, and whimsical storytelling. Let’s imagine a feline friend in the world of Wes Anderson...

Didn't Tom Waits successfully sue Frito Lay when the company found an artist that could closely replicate his style and signature voice, who sang a song for a commercial that sounded very Tom Waits-y?

Yes, though explicitly not for copyright infringement. Quoting the court's opinion, "A voice is not copyrightable. The sounds are not 'fixed'." The case was won under the theory of "voice misappropriation", which California case law (Midler v Ford Motor Co) establishes as a violation of the common law right of publicity.

Yes but that was not a copyright or trademark violation. This article explained it to me:

https://grr.com/publications/hey-thats-my-voice-can-i-sue-th...

…in the US. Other countries don't have fair use.