For the most part, I'm opposed to the idea. I like the variability brought by dice.
Like most things, though, there are exceptions. Most notably, I might apply something like this to the player who never digs out his damage die until it's time to roll it, then puts it back in his bag, thus condemning the rest of the group to 60 seconds (or more) of lag every round. It might also get thrown at the mage who doesn't bring enough d6 for her own fireball.
Regardless, if I did use it, it'd be actual integer average, not rounded to the closest 5. 1d6 is 3, 2d6 is 7, etc. Closest 5 takes it into that unholy realm.