I think this is an excellent structural analysis of the Manic Pixie Dream Girl problem.
Inebriated Spook: What Ennui Hath Wrought, Part One
How she functions, I'd argue, is as a source of direction. The Manic Pixie Dream Girl, regardless of whether she has blue hair or pink hair, whether she wears vintage sweaters or Doc Martens, is in the movie basically as a catalyst, a plot device to kickstart the main character's inert life. Her personal traits are totally irrelevant to this fact; she could be anything as long as she gets the catalysis done. A Manic Pixie Dream Girl is a cross between a messiah and a muse: she not only inspires, but she does it at a moment of dire need, when the protagonist is so stuck, professionally, and emotionally, that inspiration is basically interchangeable with salvation. All of which is to say that she can't exist in a movie that doesn't have a directionless protagonist, and that the Enemy in her movies—the force so evil and all-encompassing that only outside salvation can defeat it—is inertia itself. Not just unleaded plebeian inertia, either, but the high-octane moneyed twentysomething variety. Without inertia, she has no in. And the corollary of that is that if the movie is about inertia, she will appear. Any movie about educated twentysomethings that is fundamentally about one man's struggle with inertia, and has a major subplot that is romantic in the conventional sense, will tend to produce Manic Pixie Dream Girls.
So now we have not only a definition but a way of predicting when a Manic Pixie will show up—and also, we're no longer just talking about this particular character archetype, but rather the whole style of screenwriting that created her—that is, screenwriting obsessed with inertia, awkwardness, and "finding yourself."
This sector of screenwriting is what gave us the careers of Judd Apatow, Noah Baumbach, Michael Cera, Jesse Eisenberg, Lena Dunham, and a lot of others, and it cleaves pretty closely to their general style. It's preoccupied with adolescence, ennui, arrested development, lingering family issues, and the utter inability to cope with the choices provided by privilege. None of this is new to screenwriting or narrative in general, though—John Hughes movies are often about these issues, The Graduate certainly is, and, of course, so are Portrait of the Artist as a Young Man and Augustine's Confessions.