...I guess we love to classify people outside of fiction as well, but I'd rather not go there just yet. ^^;
Anyway, I was thinking about things like Hogwarts houses, or the factions in Divergent, or even the Four Nations in Avatar, to an extent-- why do we like to do that? Separate people according to personality and interests; making sure they spend their formative years surrounded by the like-minded?
I would say that Avatar is an example of 'classifying' done right, actually: it's never implied in the story that anyone who acts a certain way belongs to a specific nation; there's always a larger cultural force behind any conformity (like the Air Nation's philosophy, or the former Fire Nation's propaganda).
I only include it here because fans treat the Nations the same way as the other systems: if you're aggressive and hotheaded, you're a firebender; if you're easygoing and carefree, you're an airbender, etc. ^^; They insist on watering the concept down to yet another personality quiz. Why, though??
I offer three answers:
1) It's fun. ^^ Humanity collectively has done it over and over throughout history (the four humors, zodiac signs); it's only natural that we'd enjoy building stories around the concept of all the characters fitting into cute little boxes. Plus, it offers an easy opportunity for reader interaction: they can try to figure out which little box they might fit in! =D
2) It makes a good foundation. So many stories center around the hero leaving familiarity behind and venturing out into the unknown, and an easy way to set this up is by starting them off in a place where everyone has one big obvious thing in common. Then maybe they meet other characters from places where some other big obvious thing is the norm, and expand their worldview.
3) 'Like begets like'. If you start with a diverse group of characters and work backwards, it's easy to imagine that each one came from a place that molded them into the person they are, right? Kinda like when people design the MC's parents to look like them; so you can easily tell where they 'got' all their own features from.
Of course, this isn't realistic: a person can live in a country without exhibiting its stereotypical behavior just as well as someone can have a child that doesn't really look like them. But, y'know, it's easier to take the obvious route. ^^;