The challenge I see is that (in the US at least), "style" is not copyrightable in the arts. IMHO this is a good thing because artists learn and copy from one another, and if it were copyrightable that would lead to no end of lawsuits between media companies. So my concern is trying to apply copyright to training AI models can easily slippery slope into more draconian copyright rules for human artists.
I don't think there is a slippery slope in the foreseeable future, unless you buy into sci-fi views of AI being like a human. We need to update the laws around copyright in response to these machines. It's similar to why copyright laws exist in the first place: the concept was developed in response to the printing press. At some point there will be a real I, Robot problem about an AI artist that actually understands…
Style is also very broad. It’s even harder to determine whether an 8-bit NES sprite is in the “old Nintendo” style, because 8-bit sprites don’t have much flexibility to distinguish themselves.
Broadness: imagine if whoever first came up with the “low-poly 3D” or “flat material” or “voxel” aesthetics could copyright them and prevent anyone else from selling anything in those styles. What defines a style as narrow enough that it can be copyrighted? And what if that definition changes, e.g. if a a specific voxel style gets copyrighted, then someone else discovers a brand new way to render voxels super efficiently in only that style?
Objectivity and similarity: an artist can make a concrete object or character which is very similar to a copyrighted one but also clearly distinct. This is very important, because if “similar” objects could violate copyright, where is the line when something is dissimilar enough? Ultimately it would be very far for small artists, who can’t afford to risk lawsuits; vast swaths of clearly not similar characters and objects would be blocked off from them, because in the eyes of the law and without good representation, they’re no longer “clearly” not similar. In fact, it may be hard for an artist to even come up with an object or character that doesn’t risk a copyright lawsuit, since there are more copyrights that anyone could fully know. (At least to my knowledge, with copyrightable characters and objects this hasn’t been a frequent issue; but if it is, copyrightable style will make it worse, so for the sake of the argument...)
Copyrighting style is basically copyrighting the “similar” works. There’s a fine enough line between whether a character or object is “similar to” or “the same as” another (again to the best of my knowledge). But there’s no fine line with style. If one tries to define a style with objective criteria like making their “style” a specific stroke thickness and color scheme, generative AI users will just create art which falls right outside of this criteria. If one tries to use an AI classifier (ironically) to deduce whether something is “the same” or “similar but distinct”, it will be foiled by AI-adversarial manipulation and its effectiveness will be endlessly disputed in court. And if one defines their style with very subjective judgements, that leads to the issue above.