No, it wouldn't. Because if I record "Revenge of the Sith", compress it, and then distribute it for free online, that's obviously not fair use.
Fair use is pretty complicated. Part of Fair Use is the "The Effect of the Use on the Potential Market for or Value of the Work", which already puts even human commercial endeavors in a tough spot. You can make it work, but you have to really try. Satire like Weird Al or whatever isn't competing with the music it's satirizing, the venn diagram between those markets barely overlap. But a lot of LLM use cases are explicitly meant to obsolesce and siphon value from the things they used.
Like, why go to Getty Images when you could instead go to the glorified database, which has ingested all of Getty Images, and acquire an indistinguishable stock photo for free?
The only reason we're even really entertaining this is because people continually draw parallels to humans. You see, it's not stealing from Getty. It's more like if someone saw Getty Images and then went out and took a photo in that same flat, boring style. Except nobody saw anything. And nobody went out an took a photo.