And Australian (and New Zealand as well) cities' mayors are apples and oranges when compared with US cities' mayors. Sure, he sits up and rolls the ball for the day, but unlike US cities' mayors he doesn't command police force, education, firefighting, and even "social welfare". All city councillors are as powerful as him in council meetings.
Actually San Diego has that sort of government. Our mayor is little more than one extra vote on the City Counsel.