There is literally not one single piece of art that is not derived from prior art in the past thousand years.

This is false. Somebody who looks at a landscape, for example, and renders that scene in visual media is not deriving anything important from prior art. Taking a video of a cat is an original creation. This kind of creation happens every day.

Their output may seem similar to prior art, perhaps their methods were developed previously. But the inputs are original and clean. They're not using some existing art as the sole inputs.

AI only uses existing art as sole inputs. This is a crucial distinction. I would have no problem at all with AI that worked exclusively from verified public domain/copyright not enforced and original inputs, although I don't know if I'd consider the outputs themselves to be copyrightable (as that is a right attached to a human author).

Straight up copying someone else’s work directly

And that's what the training set is. Verbatim copies, often including copyrighted works.

That's ultimately the question that we're faced with. If there is no useful output without the copyrighted inputs, how can the output be non-infringing? Copyright defines transformative work as the product of human creativity, so we have to make some decisions about AI.