Well, you could have a time dependent event, like saving a princess before a certain time has elapsed. Then, depending on the success or failure of that goal, other plots unfold.
If it was just a case of save the princess before the clock runs out or that's it: end of game, then that's not very engaging and very poor roleplaying, to boot.
If the narrative bifurcates at that point -- e.g. if that actually provides a better LS ending if she is killed, even if in the short-term it would worsen the LS position in the game -- then this is good roleplaying.
No chance they'll ever implement it, unfortunately, though.