When learning is sufficiently atomized and recombined, creations cease to be "derived from" in a legal sense.
A lego sculpture is copyrighted. Lego blocks are not. The threshold between blocks and sculpture is not well-defined, but if an AI isn't prompted specifically to attempt to mimic an existing work, its output will be safely on the non-copyrighted side of things.
A derivative work is separately copyrightable, but redistribution needs permission from the original author too. Since that usually won't be granted or would be uneconomical, the derivative work can't usually be redistributed.
AI-produced material is inherently not copyrightable, but not because it's a derivative work.
Token prediction is a form of "learning" that is reinforced by the goal of reproducing the correct next token of the work, rather that acquiring ideas and concepts. For instance, given the prefix "Four score and seven years", the weights are adjusted until "ago" is correctly predicted, which is a fancy way of saying that it was stored in the model in a lossy way. The model "learned" that "ago" follows "four score and seven years" exactly the way your hard drive "learns" the audio and video frames of a movie when you download a .mp4 file.
I dispute the idea that token sequences reproduced from the model are not derived works.
I predict, no pun intended, that a time is coming when the idea that it's not a derived work will be challenged in mainstream law.
The slop merchants are getting a free ride for the time being.