I always got the impression that everything Q did was simply irritating. Winn made decisions that actively risked people’s lives because she was looking for career advancement. She was actually a threat.
Also they kind of knew that Q wouldn’t actually allow anyone to get hurt because he probably wasn’t allowed to.
It wasn’t the actor’s fault, he was given absolutely nothing to work with. Every time I’ve seen him in anything subsequently he’s been a likable character and a good actor.
I really don’t know why his character was on the show the writers clearly didn’t have anything for him to do.