Actually the burden is to prove that what AI is producing is plagiarism or copyright violation, this isn't about some special right, but that there are many making the case that things produced by AI are duplication of their work.

I'm also not sure where the concept of "the tool" be given a right to anything, That certainly isn't my argument, the right of the work should be to the user/owner used to create things with the tool. There are several pieces in the SFMOMA that use automation to create art, that art is credited to the creator of the machine, not the machine, I see AI in a similar lens.

You are intentionally selecting a device that makes duplicates of things as your comparator, so I can't tell if that is biased or some sort of flaw in your argument.

But an LLM being trained on works, and generating something based off of that training is not a duplication of any specific copyrighted material, and is wholly unique is not duplication.