Are we afraid of flawed characters?

I supposed I should have titled this "are we afraid of flawed female characters," but that's a topic that's been explored by feminist and non-feminists alike (and personally one that I don't think requires feminist analysis, but seems to be most acutely viewed through a feminist lens), but in a more general way, do audiences want flawed characters? What about when those characters are also members of marginalized groups? It's important, for sure, not to fall prey to stereotyping, but conversely there's definite pressure to make them "good." I'd rather watch or read a fully realized, yet completely unlikeable character.

Most of my favorite characters are flawed. Not bad, per se, but unlikeable. Sometimes patently unlikeable. For the sake of simplicity, let's stick to TV. I know it's not popular to say this, but I like Girls. I didn't want to. I bought into the hype that it was a show about four entitled, self-absorbed twenty-somethings, none of whom are spectacular in any identifiable way except their status as people privileged on almost all axes. This is not to say the lack of diversity on the show isn't a problem, because it is, but a lot of the criticism went much further than that, and the overwhelming consensus was that they just aren't likable. And since none of them is sympathetic enough to be considered an anti-hero in the classic sense, it confuses a lot of viewers accustomed to very obviously drawn lines between good and bad.

Looking followed the same pattern of having all the possibility in the world to be a great show, but fell short in most people's eyes. Patrick is a quintessential nice guy in a lot of ways, simultaneously unaware and hyperaware of his own prejudices and shame, and by the finale, showed little growth. (Personally, I think stasis is undervalued as a plot device in television.) You see a lot of this in fiction (in fact, it's a big no-no to wrap everything up in a nice little package -- ambiguity is good), but it's rare on TV and when it is, it's always criticized.