Anecdote: I was rolling some NPC stats last night for a campaign world I'm working on. I was rolling for a minor cleric (level 3, which is not minor in itself but this is the cathedral) of the Church of Law in the main city-state of my campaign region. I came up with terrible strength, low intelligence, terrible constitution, but a stellar wisdom and amazing charisma. Answer: this is a "gramps" character. He never rose high in the Church because he had neither the natural wit or ambition, but he's an excellent pastor and savvy about human nature; he is the most beloved figure in the local Church.
My point is, bad scores contribute as much flavor as good rolls. Even though this is an NPC, the same holds true of a PC. If I rolled such a character at level 1, he could still be a beloved and grandfatherly fellow who was an acolyte and is now taking up the cause (perhaps he was in charge of a minor shrine for many years, but now has been replaced and instead of retiring has decided to go on a crusade, or whatever). Is the character handicapped? Sure. That's fun in D&D. I don't think it would be fun in something like Exalted (just like nobody wants to play Aunt May in a Marvel Supers game) where people jump over mountains and kill 15 godzillas per encounter or whatever it is, but in a relatively more down to earth setting there's a chance for Gramps to do something useful. And hey, maybe he will have a meteoric rise to uberness. Or, maybe he will end up slain on level 4 of the dungeon. Gramps is a "high stakes" character: he's either going to win big (i.e., at all!) or lose big. Chances are, the group will get a big charge out of him either way.