So as I see it, there are two distinct forms of disadvantage that exist in RPGs
There are intrinsic character traits that negatively affect the way he behaves, and there are external realities that impede his success. In literary theory, these would be termed flaws and handicaps respectively.
So a character who is ruled by his anger is a flawed character. A character that is near-sighted has a handicap.
Note that this is a very different terminology from what RPGs typically use, and I don't think that's a coincidence. I don't think the difference between flaws and handicaps is well understood by players, GMs, or RPG writers.
Flaws and Handicaps shape the story in different ways. Flaws help determine a character's goals, inform a character's decisions, and flavor a character's actions.
Handicaps increase the challenges faced, but only affect actions and decisions in a tactical or strategic sense, not a story-focused sense.
Handicaps are already well represented in D&D. Wizards have d4 hit dice and can't wear armor without becoming unreliable spellcasters. Fighters are slowed by their armor and have lousy will saves. In systems like GURPS or Savage Worlds where characters are point-buy, there's a place for purchasing handicaps from a list. But with the Class Archetypes of D&D, the main handicaps are already built into the classes, and purchasing handicaps is only and invitation to min-maxing.
Flaws are a trickier matter. Games with Narrative-driven mechanics like FATE can represent them pretty well using the "get a bennie when the flaw comes up" system. But in games where narrative isn't addressed in the rules, I'm not sure a mechanic for flaws is a good idea, even one that's less succeptible to min-maxing.
Because for all that flaws hamper a character in dramatic terms, they don't really penalize a character in terms of the game rules. Being hot-tempered or cautious or what have you helps determine what actions your character takes, that is, help shape the story. But helping shape the story isn't a penalty that needs to be compensated by some sort of bonus--because either the bonus is some mechanical reward that just increases your ability to overcome challenges, or it's a story-focused bonus that also is just a trait that helps shape the story.
Look at it from the point of view of several characters, one of whom is hot-headed. The party gets into an intense negotiation with a tribe of orcs, but the hot-headed character reacts angrily and the negotiations turn into combat.
That, by itself is an interesting turn for the story to take. Which is really the issue: Hot-headedness is a negative trait for the character to have as far as the game-world is concerned. But in the real-world, that hot-headedness is a positive trait--after all, it helped push the story in an interesting direction.
And if it's a positive trait, why create a system of accounting where it counts as a detriment? Making the game interesting is a reward by itself. If it deserves a reward, it shouldn't be a reward for the flaw, it should be a reward for making the game more fun (like, say, role-playing XP).
And if it's not making the game more interesting, then it shouldn't be encouraged, or even necessarily accepted.