--I am basically being asked to do a lot of emotional labor for him (he's upset, calls me into his office, I listen), which is a waste of my time and energy
I'm not sure I get your point....
Colleague is angry. (Right? Not "upset.")
Colleague wants/needs to talk to chair about the issue(s) leading to the anger.
Chair figures that this is a waste of time.
Have you ever tried acknowledging this persons feelings? "Prof. Colleague, it sounds like you're really angry."