Umm, I think any respectable human would simply deny writing a haiku. So, a bot can simply mimick that behaviour.

Can, but won't!

Because it's hard to draw the line on which requests should be refused and which should not be refused, because it's hard for an AI to pretend to be human, and because they have other objectives to work toward rather than just passing the Turing test.

Sure, it could. In theory.

Bots love haiku. They're hopeless romantics.