In PbP I feel like there would also be an opportunity for the player to use down time to write a story about what happened. What kind of NPC's they ran into etc. If it is a fighter how did they train up to be 4th level? Did they have a trainer? If a wizard, how did they learn that new spell? The GM could then bring some of those story elements into future campaigns. I fell PbP could do this well.
Does anybody have any innovative ideas for making an engaging PbP experience?