Had it a while back where a husband ran all the way to the gate to tell us his wife is just behind him,I said ring her and tell her to walk,we will wait!!!made the time up in the air.
With regard to a single pax being at the gate -10mins etc,If it is only 1 person,then what can be done,but if it a few people then its a trend and I would wait,Particularly if they checked in bags(evidence they are actually here etc).