Neither of them have to be CEO. So Page and Brin can reward the CEO for being ruthless in a down market and also have Sundar be the scapegoat for them. The “cake” is their stock going up. “Eating it too” is the CEO scapegoat.
With controlling the majority of the votes, other shareholders have no ability to vote out the board. This isn’t about them being on the board. It is about their absolute control of saying who is on the board.