Except they aren't copying it, but instead drawing inspiration from it. Which all humans have done forever.

This falls apart for 2 reasons. First, I don't think there's any technical definition of "inspiration" that applies to a deeply nested model of numerical weights. It's a machine. A hammer does not draw inspiration from nails that have been hammered in before. Second an AI is not a human under the law and there's no reason to think that an activity that would be considered "transformative" (e.g. learning then painting something similar) when done by a human would still be considered such if performed by an AI.

Following your logic: if AI is like humans why don't we tax its work?

If an AI ever gets paid for the work it does, I'm sure we will.

Bad argument. Copying art is not the crime, distributing the copied art is the crime. The Disney Gestapo can't send storm troopers to your house if your kid draws a perfect rendition of Mickey, but they can if your kid draws a bunch of perfect renditions and sells them online.