LLMs are stochastic. If I send you the prompt instead of the output, then there's no guarantee that the output you get will be correct. If I generate the text myself, I can verify that it's correct before sending it off.

The problem is that as the recipient, you have no idea whether I've even read the output, let alone verified or understood it. And with the low barrier to entry, it's much more likely that you're getting unverified slop. Sharing the prompt isn't going to help with that.

Edit: sorry, posted before I finished writing.