Savage Worlds does this right with wounds. Anything under a great success leaves the character shaken, so that they must save of lose their turn. Every wound is a cumulative -1 on all rolls. 4 wounds and you’re out of the fight.
I’m really singing its praises here, but I really love the classless edge system of Savage Worlds. I’ve never come up against the problem I have with other RPGs where I have to force the mechanics to fit my concept. Want a plate armoured wizard? 2 edges, playable as a beginner character.
That sounds neat. I am so completely bone tired of the "my character comes online at 6th level" dndism. It doesn't have to be that way! You can have fun now, not in six months!
Please give it a spin if you haven’t already. Game mechanics need not be constrained to die roll plus modifier. Probably my favourite mechanic is that your level of aptitude in a skill is repesented by the size of die you roll. Also, Savage worlds were doing rerolls for good roleplay in the form of bennies for a few years before D&D dreamed up advantage and inspiration.
It's been recommended to me a bunch. It's on my list, but after Fate. I really want to have a solid game of Fate, but unfortunately I am not yet a grandmaster of Time.
I've played and briefly GM'd both. They share a lot of stuff while feeling completely different. Savage Worlds is wild and unpredictable, with some narrative control in the hands of the players. FATE is a lot more predictable, with a strongly centered bell curve on rolls and higher narrative control with the players. I love both for different reasons.