With respect to practice, I practice a drill where a line is tied from the back of a vehicle to a 5 gallon plastic oil pail. The action begins at about 20 yards as the vehicle accelerates away, and you try to hit the pail as it jumps and rolls towards you. This trains you to quickly manipulate the bolt of a rifle (if you are so armed) from the shoulder. It also demonstrates you that you are very prone to shooting where the target was - not where it is.

Mark Sullivan doesn't need me as his spokesman, but his logic for waiting seems to be that although moving there is less chance to miss the animal at very close range. Over the years he has had the opportunity to refine this technique to a degree which most of us would be unable or unwilling to intentionally emulate.