One of the ways I think about this is to treat AI as if it were another person. If I want to give information to Bob but I think Alice might do a better job of writing something, I'm not going to ask Alice and then copy-paste her response to Bob. I'd either tell Bob to ask Alice, or loop Alice into the conversation. Me being the middleman between Alice and Bob can cause several issues including delayed communication, miscommunication, and obscured provenance.
Alice being AI or a real person doesn't change those factors much.
I think this is a reasonable position, I prefer when people separate their words from their agent's words clearly, but I don't have a problem with reading stuff other people's agents wrote if the input to the writing was really good. I don't need to see the prompt, not having your agent Cyrano me is enough.