You're begging the question that OP is going to randomly punch people and has pathological rage, not justified anger as they described. It's OK to be angry about something that can and ought to change.
We trust people to do specific things, not a general trust percentage for all tasks. We aren't suggesting someone who's angry at the system to be your brain surgeon, because then it serves no constructive purpose. Meanwhile an unempathic brain surgeon might not be the best to hold office.