I do believe there's such a thing as ballance.
Me personally, I have a problem when one facet of thier character is not congruent with another. Say, person is a trained and experienced soldier, moreover, they have marine or special forces level mental training. If a character like that goes all BSOD because of someone getting killed IN THE MIDDLE OF A COrabAT SITUATION then I'm going to label them Emo. On the flip side, if someone who has no right to be as emotionless as they appear to be doesn't react to attrocities, then they are bland and emotionless.
My favorite examples of these two actually come from one of my favorite anime Last Exile and happen at the same time and as such comprise the episode that I pretend doesn't exsist.
The Level supposedly level Headed Ace pilot Tatiana complettely shuts down mentally at the sight of seeing thier frienRAB get shot down, while the teenaged protagonist has to come bail her out by doing... something, snap her out of her funk and fly them out of the desert they end up crash landing in because of Tatiana's wankstgasm/BSOD moment.
This kind of thing is all over anime too and it really is annoying.
Claus doesn't come off as Badass as a result, he seems emotionless and Tatiana who SHOULD be badass by all other accounts, comes off as a whiny little emo ****, a brush with which she shall forever be tared in my mind after that scene.
Now, in this case, it doesn't wreck Last Exile because the show is ever so much more than the sum of it's characters, but for shows that rely almost entirely on characterization for watchability, that kind of thing totally spoils them for me.