Rarity is a type C in The Killer Rarityverse fic The Secret life of Rarity, in which she maintains her social life over a period of 16 years in which she murders over 100 ponies/other races. She starts to slip towards the end, leading to her confrontation by Applejack
In the fanfiction Composure, Princess Celestia is so trapped in her own image of composed benevolence that she breaks when Luna attempts to get her to acknowledge her feelings, releasing a millennium worth of repressed emotions all at once.
The receptionist of Eve Hill Corporation in the Lilo & Stitch fanfic Aliens! does everything with cheer and a smile. Including knocking Jumba unconscious for snooping around.
Ruth in Sonic the Hedgehog fanfic CIA Agents is clearly a Type A, she is so affected by her parents' divorce that ends being obsessed with the photography rather than just taking it as a hobby.
Though it's just as common for the "idiot facade" to be the only think keeping him sane from the abuse he receives from almost everyone (which is usually a lot harsher than canon, with mobs beating him and sometimes even being raped).
Invader Zim fanfics about Keef are pretty rare, but those that exist often portray him as having neglectful of abusive parents. Given Jhonen Vasquez' style, this is entirely plausible (compare Squee, for example.)
Draco Malfoy often gets this treatment in sympathetic fics that don't actually put leather pants on him. I.e., he's spent his whole life trying to be what his father expects him to be and has no idea what he is. More of a Stepford Smirker, of course, but it's entirely possible he does smile at people who aren't Harry Potter and his friends; we'd never know.
In the few fics that actually center around and/or care to develop Big Macintosh from My Little Pony: Friendship Is Magic, he's generally portrayed as being a Type A or B for one reason or another. Hinted at in the example below, from the heretofore-unfinished shipfic "Like I Imagined":
Applejack glanced at her friend. "Usually he's just all plain an' sleepy-like, but sometimes he gets this look on his face like..." "Like?" Rarity echoed. "Like there's a bunch a' gears workin' in his noggin." Applejack frowned. "An' I don't much think I'd like to know what they're puttin' out." "Why not?" Rarity looked over, concerned. "'Cause when he gets like that, he looks darn near fifty." The earth pony shook her head. "It ain't right for a colt to look twice his age."
Til You Feel It All Around You reveals that Usopp was already developing into one of these at the tender age of seven. At one point, when Sanji affects a false cheer to try and reassure his temporarily deaged nakama, Usopp shows him how to 'fix' it and smile more convincingly. Sanji's rather freaked out by the demonstration.
But he got it now. He got what everyone was looking for. It wasn't for him to be happy, and he wasn't trying to be mean thinking about that. People wanted other people to fit into a nice, neat package with smartly tied bows that were the right color to match the wrapping paper. People wanted to be able to classify other people, and for them to behave according to code.
Light found his code.
His role is son, older brother, protector, student, genius, role model, kind, earnest. His role is to be perfect so they don't have to worry again, so they won't say he's abnormal, strange, worrisome (all whispered in the dark night across the kitchen table when they thought he was asleep).
Light: Class ended and before I could even move from my position, females (if they could be called that) flocked my surrounding table. It was utterly disgusting. I casually said a pleasant goodbye to Ryuzaki before being escorted off to the library to help out a fellow classmate. I would rather slit my wrists and write my own name in the Death Note, but sacrifices had to be made to maintain my identity as the perfect individual.
The Star Wars AU series "Sith Academy" initially portrays young Obi-Wan Kenobi as pathetically cheery and happily co-dependent in a rather sick relationship with Qui-Gon. It eventually got to be too much, so authors decided to explain his demeanor as the result of a super-Prozac drug called Perkium, that was being used to medicate the formerly rebellious punk padawan into perfect Jedi conformity.
In A Charmed Life Light is very emotionally stunted so while he thinks he's alright in reality he is actually quite miserable. Ryuk and L are the only ones to ever figure out what's Beneath the Mask and Ryuk is the only one to never judge him for it.
In Amazonian AWOL Blaise Zabini does his utmost to maintain a cheerful front despite the fact that his ex-wife is draining him dry financially and he's on his last chance with his boss.