I’m not sure this argument is correct. You can sign whatever contract you like with the model provider, right? Including “you are entitled to the end product but not the intermediate scratch work”?
Coming from a place of genuine curiosity: is there some precedent or statute that would invalidate that contract? I don’t see why the reasoning tokens belong to you.
For example, I pay lawyers by the hour but don’t necessarily own their meeting minutes, recorded discussions, research notes, etc.