The thing is, we appreciate art not just based on qualities of the final product, but also based on how it was created.

Do we? Marcel Duchamp springs to mind. He’d just pick up an object and declare it art. Piero Manzoni shat in cans. If that’s a creative process, I am positively proliferous.

This only supports the argument that it's not the qualities of the final product that make something art.

I disagree, but even if I let you have that point, what about Cariou v. Prince? If taking a photograph of someone else’s photograph is legally considered a novel work, then how does AI differ?

https://en.m.wikipedia.org/wiki/Cariou_v._Prince

Well, apparently, it differs in the sense that people don't call the final product art.

They do.

https://en.m.wikipedia.org/wiki/Appropriation_(art)