While the idea — of shuffling a societal system a little bit to prevent it from going stale — sounds important, I'm not convinced. Random shuffling leads to good results only when it is combined with a good fitness estimate (see: natural selection). And establishing a fitness test for a societal order seems to be a much harder issue than than that of an organized randomization.

Much of the fitness test can be from self selection (you apply for a random spot.) Many people wont bother to apply.