Nier sort of does this with New Game+ - basically, on your third playthrough, you can choose (as part of the game's plot) to sacrifice yourself, erasing the memory of the main character from the minds of the other characters...and deleting all your saves (intentionally). It also won't let you use the same name again.
More of a meta extension of the events of the game, but still, it does add a lot of weight to making an in-game decision.