I think they would give a great reason to replay the game. At the moment I saved multiple times and replayed to save different people or get different outcomes but it isn't very rewarding without some feedback from the game, and it's a shame because it makes players think there's less from this game than what there actually is. And also achievements would guide me better on what to do and what event to replay instead of mindlessly trying out a thousand times if something is possible on a scripted battle.
It's not that much to implement and it would improve replayability a lot.

(I haven't found a feedback page on this site so I wrote it here)