I think the criticism about resource randomness in regards to Monarch Power is to some degree fair, though I also think the randomness adds a certain emotional layer to the flow of the game - you care about your monarchs and your heirs to a much greater degree than you otherwise would. I also think that if the resource randomness *really* bothered people that much, republics would be far more popular than they currently are.
The only degree to which I ever REALLY cared about my monarchs and heirs is how mind-blowingly STUPID the monarch has to be to be unable to figure out the line of succession and whether or not there will be an heir if he decides to stick the current one in an army to die.
Oh, and the gross erectile dysfunction of Ming emperors, because the Muslims need only 4 wives to have +100% heir chance and the average Chinese emperor has 40+.