Definitely it doesn't change the fair use argument, but it should change the way we talk about these companies and the way we contextualize what they're arguing and the way we talk about the surrounding debate. We should be up-front that there are plenty of examples where people are not granted these fair use rights and that fair use is often unequally applied to IP law.
And we should be pushing hard for the entire package (not to say that you're not, more just pointing out that this is a package deal) -- I am not a copyright maximalist, but I especially don't want a model where only artists and individuals are subject to copyright restrictions. I'm of the opinion that it is good for these companies to take a credibility hit for their hypocrisy and for us to make it clear that the fair use argument has to be something that applies to everybody. I hope that this hypocrisy is something that comes up in court if these lawsuits go through, and ideally I'd like it to become a sticking point where trying to have their cake and eat it too does hurt these companies' legal arguments.
I want limited copyright across the board, but a system with maximum fair use for companies like OpenAI and minimal fair use for consumers and individuals is worse than a system with expansive copyright for everyone. I think it's a good thing for companies like OpenAI to be unable to make selective arguments. We shouldn't treat their end goals as irrelevant.
It's also very true that there are open models that take a permissive approach, but those models are in my experience usually not the primary target of most criticism (outside of the "open models are dangerous" FUD). The linked comic explicitly calls out "profit-making companies that own the most-used channels of communication." I'm not sure the artist would phrase it this way, but I think reading between the lines the artist is very likely coupling together ownership with their complaint -- they are talking about the injustice of having their work appropriated into a form that is locked down and controlled and that exists for the benefit of the profit-making companies who want to own yet another channel of communication (in this case artistic communication itself). I suspect that part of that feeling of injustice does directly come from an understanding that as an individual anyone would be sued into oblivion if they tried to make the same arguments in the opposite direction.
Does that get rid of the fair use argument? No. But it is impossible to actually talk about the fair use debate in a useful way while ignoring the context of that debate. To just mention fair use and nothing else is leaving out a ton of context about why artists are mad, and about why this feels unjust to so many people, and about the regular inconsistencies in how these arguments are often applied. We don't have to get rid of fair use arguments, but I personally think it's more responsible to include that context. I worry that leaving that context out is playing directly into the hands of companies that are trying to create an outcome of selective enforcement for IP.
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It's a bit of a sidenote, but on the subject of truly open models, I will say that it is great that those models are licensed the way that they're licensed, but I'd still rather have legal recognition that algorithmically generated weights are not subject to copyright at all. It's nice when companies are permissive, but it also subtly implies that they have a choice whether to be permissive. As someone who favors expanding fair use, I would prefer that they not have that choice. I disagree with the application of any license to model weights, permissive or not. I think at best those model weights could be subject to a database license, maybe, but I'm honestly a little skeptical of even that: I think that model weights are a factual and reproducible artifact of training, not a creative work.