OP, as You did not mention the type or general situation you are referring to, maybe You could write a few words on why a shutdown after clearing of the congested area is necessary or beneficial? Are you taxiing out for departure or are you referring to a mere relocation of the aircraft on the apron that is for whatever reason done under its own power and not by tug?
One thing that needs to be remembered as well is that not only fuel costs money, but so does an engine. A startup is not exactly easy on the engine and it may well be that the additional maintenance costs due to the number of startup/shutdown cycles racked up by this practice will be way larger than the possible fuel and brake wear savings...