My own observation is that twelve is commonly used by people to understand and quantify the world. It is used to create separations that describe the cosmos and the passage of time. These things occur at a regular interval or are otherwise fixed, standardized or sacred. There really isn't much call to randomize these things in an imagined world.
One area that comes to mind here that I think is being overlooked and makes complete sense to me when considering the paragraph above it that of the combat round. In the games I currently play Castles & Crusades and Pathfinder the combat round is 10 seconds and 6 seconds respectively. In Basic D&D its 10 seconds and in AD&D its 60 seconds (a whole minute)!
I am suggesting that in systems that use a d6 (D&D, AD&D) or d10 roll (C&C) use a d12 instead. In the Castle Keepers Guide it suggests that the use of a d10 is preferred over d6 as each value represents the segment that action occurs in. Looking at it like that I feel that it would make sense to divide the time into twelve segments, like the numbers on a clock or the months of a year. In any case the d12 would have a new lease on life.
