Artist is dominating AI-generated art, and he’s not happy about it

What if the model is already open sourced and out in the wild? It appears that Stable Diffusion included this artist's work in it's training data.

No, imagine if that was what a trademark allowed you to do, to disallow usage of that word altogether. Apple would be able to force shops everywhere to pay them or stop advertising the sale of Apples. Everytime anyone sat down to write a review of a product in Word they would first need Microsoft to negotiate a deal with the company in order for them to support the product names.

There probably is a case to be made for at least prohibiting the use of phrases like "a painting by $ARTIST" as a trademark violation (particularly if it is a registered trademark) since what is produced is not, actually, a work by the artist named, but that would still permit the use of prompts like "a painting in the style of $ARTIST".

Even if you could prohibit the use of an artist's name entirely, that wouldn't eliminate the use of their actual style per-se, users would just have to refer to it some other way, such as using a prompt like "dark necrofetishist biomechanoid style" instead of "in the style of H. R. Giger".