The other option, Asmor, is to throw all ability scores out the window and then adjust the rest of the game down 4. That might be somewhat more convoluted, though.
I've been screwing around writing a game now for the last couple years that has no character stats so I really like this idea. I mean, I REALLY like it -
-except for D&D. Especially 4E.
Why? Not enough noncombat player-narration powers and feats. Straight up. Your two main feat types in this edition are "add or subtract a number" and "substitute x for y." Even most of your utility powers are of those two types with the occasional "make a nonstandard movement" thrown in.
Stuff like Oath of the Relentless Hunter (Avenger Utility 6) and Magpie Filch (Rogue Utility 16) are my favorite types of powers; schticks. My character does this. I don't need to roll, I just do it because that's what I do. The Vancian spell system from previous editions also gave this feel to some extent. They would be gold in a statless system because they a) help differentiate one PC from another apart from fighting style and b) support the feel of a game where the math is as minimized as possible.
If I'm playing D&D, though, I'm here because I want to figure out how to get a +87 to hit. I want to stack bonuses and crunch numbers because that's what the game encourages. If I don't want math, I'll play FATE. There's something about a statless D&D that falls into a mechanical 'uncanny valley' for me.
But I still like the idea.