But this is very obviously not what AI is doing. In essence, an LLM is taking works and compressing them and storing them in a big database, to later be reproduced with a touch of non-determinism.

It's closer to archival and compression than captioning. But they're selling it. That's a big problem - you can't just take someone else's work, sprinkle some god knows what on it, throw it in a big pot with other shit you stole, and then reproduce it later. Even if your reproduction is super convoluted and not 100% accurate.