I think they have merit, as they give a bigger picture of what the person likes about the show/game/movie and a little about themselves as well. Of course this works better with fewer characters since many of them ranked in the middle would be like you said arbitrary given that the middle of the road usually gets less thought than those at the top and bottom of the list. Character lists also work best in character driven shows like K-ON! as the majority of the show is about how the characters interact with each other, so knowing what characters people like gives you a picture of what episodes and scenes people liked more/less.
I think I rambled on enough for now.