We were talking about this in the cockpit yesterday.
The man's job was to represent us to the company. It was not his fault that the company didn't cooperate with our/his expectations. He and his team got the best TA they could, which was gross, but not due to any lack of effort.
Perhaps his error was in exhorting pilots to accept the TA. If he simply said "Here it is guys, this is the best we could get after YEARS of hard work. It's in your hands now." then all would be well, IMO.
I have zero problems with his leadership, but if he feels it'd be best to step down, that of course is his option.