As a DM I can think of no more enjoyable trait for a player to have than curiosity. With it they take plot hooks regardless of concern for their character's safety. They have to look into the burial site. They want to find out what the vizier is hiding. They desire to find out all the whozits and whatzits and whyzits. I believe it behooves all DMs, GMs, Storytellers, etc to encourage and reward curiosity. Because if you punish it, it becomes lost, never to be found again.