Thx for explaining the benefit of variance, this probably puts to bed an idea I had where miners wait 9 minutes after the last block (ignore for the moment that there's no universal time in bitcoin + dishonest miners) and then turn their miners on (this would make mining less costly).
You gain nothing by doing this. Mining is a Poisson Process. The expected time until next block is ALWAYS 10 minutes. The time since last block is completely irrelevant. If it is 9 minutes after the last block, you expect the next block will appear at 19 minutes after the last block.