Earlier quoted context omitted.
In modern cars, disengaging the clutch (or using neutral) when coasting (toward a stop or down a hill) is less efficient than staying in gear. This is because it takes some fuel to keep the engine idling, where staying in gear allows the computer to completely cut fuel flow, as long as the forward motion is keeping the engine turning.
There is nothing preventing cars with manual clutches from doing that. People going down hills with manual transmission also keep the car in gear (they teach you that). And it doesn't matter as it is not much fuel compared to the fuel used when accelerating, where automatic transmissions are less efficient. If that is the only reason for automatic transmission to be more efficient, then i doubt it is.
It's taught for safety reasons. You have more controls of the car with the motor attached.