I've been considering switching to average damage for monsters, but not for PCs. I think certain players (mind you, some of the slowest ones) would revolt if they didn't get to roll their dice.
Yeah, its not for every group. Give it a try as a DM and see what you think.
Maybe even give the players the option of doing it or not. I'm sure after a few sessions the average damage doers would convince the others of the systems merits.