AGE (sort of) does exactly this, granting a number of Stunt Points (SP) for rolling doubles. You get the number of SP showing on the Stunt Die, which also determines degree of success.
SP must be spent immediately, and there's a whole table of stunts you can pull off, but two of them are "Mighty Blow" (2 SP) and "Lethal Blow" (4 SP). But because the other stunt options give you a whole range of cool naughty word (reposition you or your target, knock someone prone, disarm, boost your defense, take an extra attack, set up a second attack, etc.), I doubt people would always just opt for "more damage."
I like this part of the AGE system in concept, and although I hate tables, I think I could memorize this one. However, I've never been able to get my group to play it.
As an aside, the chance of doubles of any kind is much higher than you think, especially once you start factoring in bonuses to the check. In AGE, those bonuses can easily hit +6, even at low levels. That monkeys with the percentages a LOT.