I'm not an expert on LLM, so feel free to correct me!
I don't think fair-use matters in any way when it comes to LLM-generated content.
LLMs don't have libraries with all the data they have been trained on. They just "read" the content, figure out the relationship between the single tokens, and work that relationship into the model.
If your work was part of an LLM's training data and a line from your work appears in content created by that LLM, the LLM didn't copy that from your work. It is more likely that the line followed a very common pattern and used the same tokens "by accident" (though by accident rather means that the preceding context within the LLM-created content and possibly the prompt made it more likely that the combination occurred.) Or the line was part of many sets of training data, so it might likely be a common phrase. Another option might be that it has been copied in the first place.
no AI has ever categorically refused to finish a prompt because it might violate copyright
Probably not. But I'm not sure whether you could prompt an LLM to deliberately and reliably create copyright-violating content.
For an LLM to know whether the content they created might violate copyright, it might need to compare the created content with the data they have been trained on.
No, you don't have any right to decide what other people do with your product as long as they get it in a legal way. And it is legal to take it from an open-access source you placed it in.
If you put content on a site that allows other users to read the content, it is legal for other users to read the content.
That doesn't mean that it is legal to crawl the site.
So personally, I wouldn't say it is legal by default.
The issue might be that you can't prove that your content has been used, unless the LLM trainer keeps records of the content they used for training.
Also, AI training (specifically, training of LLMs, which is the current hype) is not "the same" as human learning. They are very, very different processes.
As far as I know, we understand about as much about the human brain as we do understand about how LLMs learn.
So the process might not be so much different, even though the current hardware most likely is. (Well, the scope of human learning is way broader and adds context from more areas. Humans might also keep a limited library as a resource.)
If they weren't, kids would use terawatt hours of electricity
A three-dimensional computing structure with built-on-the-fly hard-wired combinational logic might be more efficient than doing countless mathematical operations on a GPU.
So if LLMs ran on a different hardware, they might be way more energy efficient.
From a practical point of view, I don't think it really matters on what exact content the LLM is trained as long as there are many datasets that aren't too similar.
It might be different if you train an LLM only on a certain type of content. E.g. if you train it on Tweets only, the output might appear to be like a Tweet.