Wrong guess,
Every aircraft is different, and on the A320, the person supervising the pushback must insert a pin in the NWS system on the nose gear leg. This de-activates the steering and associated hydraulics.
Switching off from the cockpit has no real meaning if the steering pin is inserted. Some airlines like to do it anyway in their SOP's, but I have seen no benefit.
However, it we be useful if the pushback supervisor lost its pin or if you are on a remote airport not used to push/tow this type of aircraft.
Of course it is useful to reset some BSCU glitches (carful with that, Airbus has very specific procedures in this regard).