You're analyzing the factors with respect to the output of the model, not the weights:
> The purpose and character is absolutely heavily commercial and makes a great deal of money for the companies building the AIs.
That's assuming that it's Microsoft/OpenAI. Suppose a non-profit trains a model and releases the weights for free.
> There's nothing about the works used for AI training that makes them any less entitled to copyright protections or more permissive of fair use than anything else. They're not unpublished, they're not merely collections of facts or ideas, etc.
The models aren't trained on works of a particular nature, they're trained on whatever they can find, so this doesn't really mean anything until you're talking about a specific work.
> AI training uses entire works, not excerpts.
The weights don't contain entire works. They contain statistics about entire works, but that's not the same thing. You can't find a copy of any specific work anywhere in the weights. Nobody can give you a piece of code that will decode the weights into all the original works.
> AI models are having a massive effect on the market for and value of the works they train on, as is being widely discussed in multiple industries.
That's not how that factor works (and it's the most important one). No one is buying the model weights so they can read them like a novel. Typically the consumers of the weights are software developers or content creators, whereas the consumers of the original text or image are fans.
To make this a little clearer, suppose the purpose of the model isn't to generate content, it's to generate recommendations. Then the company operating it takes a list of content anyone likes, uses the model to show you a list of all the other content you might like and lets you sort by price. Which makes it easier to find competing content which is available for less money, which increases competition. The incumbents might hate this, and it might even lower their profits, but that's not the kind of effect on the market this factor is supposed to be about.
Moreover, suppose you had a model trained entirely on public domain works. Obviously this can't be copyright infringement even if it's extremely effective at producing new works that compete heavily with works still under copyright. But if you added some specific work still under copyright to the model, it would only be a marginal difference. The effect on the market for that specific work of adding that specific work to the model would be negligible. It's the technology itself that provides the competition, not the accretion of any particular work in the weights.