The original purpose of this pump was to circulate coolant through the heater core when the engine is idling. This keeps the car nice and warm when you are sitting at a light.
Just one of a zillion Mercedes ideas that no one else has come up with.
Note that Mercedes took this idea and enhanced it to use it to cool off the engine when it's shut off.
Lots of cars have aux. fans that to pull air through the radiator when the engine is shut off but that's pretty useless without circulating that coolant through the engine block. Mercedes use the aux. coolant pump to do this.
Another use is to keep the interior of the car warm after you shut it off. Mercedes pump hot coolant through the heater core and then run the blower for up to 1/2 hour to keep the interior of the car warm while you run into the mall in the dead of winter.
Mercedes also heat diesel fuel in the winter and cool gasoline in the summer to prevent either gelling in the diesel or vapor lock in the gas car.
Mercedes Benz have probably invented 90% of the important automotive advancements/inovations for passenger cars. ALmost everything worthwhile on a Lexus LS-400/430 has come from Mercedes.