This is indeed a weak-point in the contract approach: People can't be bound by an contract they never knew about nor agreed-to.
However if they acquired a "stolen" copy of my content, then (IANAL) it might offer some new options over in the copyright-law realm: Is it still "fair use" when my content was acquired without permission? If a hacker stole my manuscript-file for a future book, is it "fair use" for an AI company to train on it?
> it wasn't the person creating the prompt which generated the movie via the model
The contract doesn't limit what the model outputs, so it doesn't matter who to blame for making/using prompts.
However the model-maker still traded with me, taking my stuff and giving me a copyright sub-license for what comes out. The "violation" would be if they said: "Hey, you can't use my output like that."
> So could I use both square and circle now? [...] a squircle
Under contract law, it doesn't matter: We're simply agreeing to exchange things of value, which don't need to be similar.
Imagine a contract where I trade you 2 eggs and you promise me 1 slice of cake. It doesn't matter if you used those eggs in that cake, or in a different cake, or you re-sold the eggs, or dropped the eggs on the floor by accident. You still owe me a slice of cake. Ditto for if I traded you cash, or shiny rocks.
The main reason to emphasize that "my content is embedded in the model" has to do with fairness: A judge can void a contract if it is too crazy ("unconscionable"). Incorporating my content into the their model is an admission that it is valuable, and keeping it there indefinitely justifies my request for an indefinite license.
> What if square party wants to re-license it to X but circle party wants to re-license it to Y
If the model-runner generates X and wants to give square-prompter an exclusive license to the output, then that's a violation of their contract with me, and it might be grounds to force them to expensively re-train their entire model with my content removed.
A non-exclusive license is fine though.