While it seems like a nice idea on the surface, it would also seem unusual to do it for just this (now quite old) quest, as this disconnect is the case in pretty much all quests from the very beginning of the game.

Game wise it would likely need a large change over the entire game, not just this quest. First, quests would need an extra state to account for;

* in progress,
* finished but not handed in
* handed in

And all quests in the game would need to look for the new state and have a switch to the existing, or even a third set of dialogue applied to possibly multiple NPCs.

This could involve more database space, more complexity, and it would involve going back and adding complication to the existing dialog branching logic that would need to be done to every other quest in the game, not just this one.

It might be personal experience, but most people do seem to hand in when they finish. I wonder the worth of adding a third state to every single quest in the game to account for completed but not handed in.

I wonder what new content would need to be cut to implement it?