3rd Edition did this. There was clear distinction between lethal and non-lethal damage. Both could take you down, but only one could make you dead. Guess which.
But this probably didn't get GMs to use non-lethal damage for "mook" encounters and lethal for "boss" encounters. Mostly because no-one really told them, I'd reckon.
And that's the problem here. System is only half of a full game - you need the scenario, the adventure, to squeeze the rest out of it. And for all its tables and guidelines, I feel D&D has never done a very good job at telling exactly what rules to use for which style of game to the GM. Or maybe it's been too long since I read the books and have been talking to too many people who essentially ignore much of what the DMG says.