I ran a game years and years ago with a custom system where every character had a list of traits, and your dice pool was just the number of relevant traits. Traits could be conventionally positive or negative, but the only thing that affected was when they applied.
So a cowardly character would get a dice when running away. A clumsy character would get a dice when they were falling over or dropping things. And so on.
I've got two examples:
1. Cortex Plus: When you trigger a weakness by yourself, you gain a Plot Point.
2. WOIN: At the end of the character creation you look which attribute is the highest and which one the lowest. Now you can choose a Trait (like a feat in D&D), which based on your highest or lowest score. Even the Traits based on your lowest attribute is an advantage in certain situations like having low Will, could make you an alcoholic but you gain a bonus against poisons.
Twilight: 2000 does this. Your attributes are higher when younger but you possess fewer skills. If you're older, you have low attributes but lots of skill. If you're young, you have ability that isn't honed.
Trollbabe is a system where you only have one numeric stat, and depending on what you are attempting sometimes you need to roll over and sometimes you want to roll under. So a low stat would be preferable in some circumstances.
As suggested up thread, any game with point-buy ‘rewards’ low stats by leaving you points to spend on other things.
Teenagers from Outspace. Low attributes meant you were less likely to "over do it" (succeed with unintended consequences the GM can go and have fun with). The game rewards the average.
Marvel Heroic Roleplaying did as well since lower attributes meant you rolled smaller dice. Sure, you had complications more often (rolling a 1), but you got Plot Points more readily as a result. Higher attributes/dice didn't. In theory that was the balancing act.
In addition to the "XP on miss" from a lot of PBtA games, there's also the fact that poor rolls or misses can sometimes be interesting or desirable. I've had moments in Masks games where I really wanted to get a poor roll purely for the drama of doing so.
So long as failures are not uninteresting or unfun, it can be satisfying to roll with poor stats.