That implies you think the output of an LLM is only a rewording of the prompt, and that it doesn't add anything from it's corpus of training data. That's obviously untrue.
Sharing information that is already in the corpus is simply not that valuable in a world where everyone has access to their own LLMs.
Of course, given that posting one is not mutually exclusive with posting the other, I would still think that posting both is the easiest way to satisfy both people who prefer to read the prompt and those who prefer the read the output.