Little good? Doesn't even make sense for carbureted engines. Those of you old enough to recall, 1st thing you do to start is to push the accelerator pedal to the floor once to set the choke, assuming automatic choke. This also pumps a good amount of liquid petrol into the carb throats via the accelerator pump. When really cold, you give it more pumps for more petrol for a very rich mixture.
A little blip when shutting down contributes nothing to a future start up in the throats and manifold. One, most of it is burned immediately. Two, any left will have evaporated by the time one returns to restart. And keeping the bowl full makes even less sense. Unless one's fuel pump is knackered, the bowl is almost always completely full. The float valve sees to that. When shutting down, the fuel pump is more than likely pushing against a closed valve. If anything, you're depleting the bowl a bit by pumping fuel out and shutting down before it has a chance to refill. I don't see there ever being enough liquid petrol to wash the cylinders, the engine is still running after all. That is simply way too rich. You would be getting more obvious problems than increased wear.
I stand by we did it because it sounds ace.