1. If I wanted to run a web search, I would have done so 2. People behave as if they believe AI results are authoritative, which they are not
On the other hand, a ban could result in a technical violation in a conversation about AI responses where providing examples of those responses is entirely appropriate.
I feel like we're having a larger conversation here, one where we are watching etiquette evolve in realtime. This is analogous to "Should we ban people from wearing bluetooth headsets in the coffee shop?" in the 00s: people are demonstrating a new behavior that is disrupting social norms but the actual violation is really that the person looks like a dork. To that end, I'd probably be more for public shaming, potentially a clear "we aren't banning it but please don't be an AI goober and don't just regurgitate AI output", more than I would support a ban.