I am no Guiliani supporter but he was doing what he was supposed to be doing.
He was doing his job and being in front of the camera and doing whatever it is that mayors do was appropriate.
These union goons would have had a better case if he was posing with a grenade bandoleer, or like JFK’s dad had gone off to the english countryside.
I agree with you that part of Giuliani's job on 9/11 was to reassure people on-camera. However, he screwed up royally on his other job, which was to ensure that the police and fire depts. were working jointly. Radios aside, emergency center location aside, Giuliani's own testimony about 9/11 indicated that he visited the impromptu command post the fire dept. set up, and then took Kerik off to establish a
separate police command post elsewhere. This was in direct contradiction to his own emergency response plans, which emphasized the critical importance of a joint fire dept./police dept. response to an emergency. Emergency responders died that day because of Giuliani's complete failure to follow the most important part of his own established emergency response procedures.
So yes, he did the camera part of his job that day extremely well. But he utterly failed on the management part of his duties.