To me, the main appeal of darker stories doesn't lie in the situations themselves (emphasis on 'main' there - I do enjoy the situations and storylines themselves plenty), but the deep character exploration that can result from it. Gundam AGE is a good example, where (coloring the next part white to hide spoilers)
Flit tries to get in touch with his childhood self, who was a much softer person instead of the genocidal, half-crazy old man the war would eventually twist him into becoming. That kind of soul searching and digging down into the core of a human being - a core that's been repressed, or ignored, or long forgotten about - isn't the kind of writing that tends to come along with Cute Girls Doing Cute Things shows.
In particular, I find tropes like 'Used to Be A Sweet Kid' and 'Start of Darkness' particularly fascinating. In both real life and fiction, I enjoy learning about who and what a person used to be before their soul (or subconscience or whatever if you want to use a less romantic word) was clogged up with so much crud. If you go back far enough in any 'bad' person's past, you'll eventually come across a time where they were a very different person (assuming they aren't just a natural born psychopath or something). Maybe you would have to go back to when they were 30 years old; maybe you'd have to go back to age 15, or 10, or 8, but the vast majority of the time you'll come across a different version of them eventually that hasn't yet been poisoned.
There's ways to mishandle this, one of these being that the progression happens too fast, with someone becoming a completely different person because of one trauma or misfortune. That definitely isn't impossible or anything, and there's certainly examples in fiction of this being pulled off perfectly fine and convincingly. What's much more common, though, is prolonged circumstances slowly chipping and chiseling away at a person's personality day by day across a period of months or years. Personality's a very resilient thing, and one bad thing usually isn't enough to instantly turn a person from a nice guy into a genocidal mass murderer.
By the same token, if someone
does reach the point where their personality largely breaks down, it's doubtful that they're ever going to be 100% the same again. That's not to say people can't heal with time (they can, and pretty quickly at that if they put their mind to it), but even whenever that healing process is over, that person will probably be at some middle point between their 'original' self and the way they were at their lowest point, with elements of both their pre-trauma and post-trauma self existing. My Vietnam War vet dad might not have horrible anger issues like he did in the '80s and early '90s, but he still has some bitterness that the completely sweet, completely innocent kid from the 1950s never experienced. A casual online acquaintance of mine is nowhere near the vicious asshole that he was around 2008-2009, but he still has a prickliness to him that the nice kid from 2002 and 2003 never had. Etc etc.
Though I'm not a huge Phantom World fan, I did like the way Koito was handled in this regard. She changes in some ways, but she's still a traumatized wreck of a person for the entire show, even after making friends and finding some happiness in life. The show doesn't go the "My situation's gotten better, so I'm instantly okay!" route. (I'm sure that she'll continue to get much better with time and become a mellow, happy person, though she'll probably always have a bit of an ornery streak that the loli in the rabbit cage was incapable of.) That's a good thing to me and adds to the integrity of the writing because it's more true to life. It's obvious that people have very little patience for Shinji Ikaris or Haruyukis, but the fact is that emotional issues are very difficult to get rid of. They don't cater to other people and just up and vanish because others might find them annoying. I don't necessarily want characters to vent and complain about those issues all the time, but I also don't want them to just shrug things off so easily that they don't feel like believable human beings.
School Days has a reputation for being melodramatic trash that's good for nothing but shock value, but I've always honestly believed that it's a very intelligently written show in that the characters' personality changes are done very precisely, very meticulously, and very believably - to the point where the series has always felt like a work of art to me. I have mixed feelings on parts of the last two episodes, but the first ten before that? Almost everything about their behavior and personality changes checks out 100% for me.
There's more I could say, but I think that's enough for one post. Good thread.
(Incidentally, I downloaded the first season of Yuuki Yuuna just yesterday. That show definitely falls into the "Why did I never watch this?" category. I'm saving it for whenever I move to my new home in a week or two, though.)