Scrapping ability scores (Unlikely Heroes project)

 So, I'm doing some thinking about project Unlikely Heroes. Having made the decision to abandon the quixotic quest to create my ideal version of D&D, I'm feeling completely liberated from D&D's rules and mechanics. They may inspire, but the no longer bind me. And what better way to put the exclamation point on that newfound freedom than by jettisoning one of the most iconic features of the game, the sacred Six Ability Scores?

It's certainly not a terribly radical idea. Despite ability score generation being the very first step of character creation, mechanically, ability scores aren't a core part of the old school D&D engine. They're a bit of color and flavor; that's all. The game would play just fine without them. It might even play better without them. You wouldn't have to worry about players who roll dismal or mediocre ones, nor those who hit the jackpot with every score above average. You don't have the player of the fighter with 13 Strength and 10 Constitution feeling forever and hopelessly inferior to the one who rolled an 18 Strength and 16 Con. 

I'm looking for a simple way to allow each character a bit of flavor and flair without all the disparity that comes with randomly rolling six scores. One possible way is if we give each character a single distinguishing trait such as "strong" or "nimble" which would provide some useful, but not unbalancing, mechanical benefit. I personally would prefer that players roll for their character's trait, though it wouldn't be terribly unbalancing to allow them the choice, either. 

If you were to observe that these traits map pretty closely to some of the traditional D&D abilities, you'd be correct, but they're applied in a very different way. Firstly, they're binary: you either have a trait or you don't; there's no quibbling over degrees of strength or agility or intelligence. Secondly, nobody gets a whole stack of benefits, nor does anybody end up saddled with a load of penalties. Each character gets one positive trait to work with, full stop. This doesn't mean that a character is necessarily "just average" in every other way; this is simply the character's most exceptional trait, and the one he or she tends to rely on in life the most. I think this actually fits pretty well in a rules-lite game of ordinary heroes, as well as a game that emphasizes player skill over character skill.

Conceptually, I like the idea. It only remains to determine the exact list of traits (How many? Should things like intelligence and wisdom be on the list?) and to figure out how they affect things in play, such that they're each roughly equal in usefulness and meaningful for any sort of character. Tentatively, I'm looking at something simple in application, such as each trait giving the character advantage on some category of action. So, we might have "strong" giving advantage on feats of strength (e.g. moving a boulder or lifting a heavy gate), "nimble" giving advantage on feats of agility (walking a narrow beam, swinging from a rope), "lucky" giving advantage on saving rolls, and so on.