"> The obvious difference is that copyleft is voluntary, while having your art style stolen isn't."
This is why it is important whether you consider that infringement occurs upon ingestion or output. If it only matters for outputs, then artists have a problem, since copyright doesn't protect styles at all, see for example the entire fashion industry.
There is a saving grace though: Artists can make a case that the association of their distinctive style with their name is at least potentially a violation of trademark or trade dress, especially if that association is being used to promote the outputs to the public. This is a fairly clear case of commercial substitution in the market for creating new works in that artist's style and creating confusion concerning the origin of the resulting work.
Note that the market for creating new works in a particular artist's distinctive and named style kind of goes away upon the artist's passing. What remains is the trademark issue of whether a particular work was actually created by the artist or not, which existing trademark law is well suited to policing, as long as the trademark is defended, even past the expiration of the copyright.
Meanwhile, trademark (and copyright) also apply to the subjects of works, like Nintendo's Mario or Disney's Mickey Mouse or Marvel's Iron Man. But we don't really want models to simply be forbidden from producing them as outputs, or they become useless as tools for the purpose of parody and satire, not to mention the ability to create non-commercial fan art. The potential liability for violating these trademarks by publishing works featuring those characters rests with the users rather than the tools, though, and again existing law is fairly well suited to policing the market. Similarly, celebrities' right of publicity probably shouldn't prevent models from learning what they look like or from making images that include their likeness when prompted with their name, but users better be prepared to justify publishing those results if sued.
You can also make the (technical) argument that if you just ask for an image of Wonder Woman, and you get an image that looks like Gal Gadot as Wonder Woman, that the model is overfitting. That's also the issue with the recent spate of coverage of Midjourney producing near-verbatim screenshots from movies.
It might be appropriate though to regulate commercial generative AI services to the extent of requiring them to warn users of all the potential copyright/trademark/etc. violations, if they ask for images of Taylor Swift as Elsa, or Princess Peach, or Wonder Woman, for example.