Even if they were allowed, I'd never have Joyce or any other exec in the cockpit during flight. I don't need distractions which just make me angry by their mere presence.
It actually is allowed- operational reasons. I can think of a few whereby the CEO could tick that box.
The reality is though is that he has no desire to see the work done on our side of the flight deck door. He doesn't rate it, doesn't value it and certainly doesn't think that anything a pilot says is worth listening to.