Getting to know Laura's character gives us more reason to care about her when she gets into trouble. It is, however, a small leap to an unwarranted conclusion.
Designers add puzzles which are difficult simply to be difficult.
Never mind advancing the plot. Never mind creating puzzles which flow naturally out of the game's setting. A locked door can figure more intimately into a story if it involves NPCs with some stake in the outcome of the story. You might simply walk up to the duchess and ask her for the key. The IF programming concept, as first implemented, is good at dealing with physical objects.