The biggest problem is that it can wreck the evap system. This collects gasoline fumes from the tank and routes them to the engine for combustion. Overfilling could force raw gas to enter the system and prevent it from working right. It could also cause a condition where you have a hard time filling the tank, as the system can't properly relieve pressure from the tank and the gas pump's automatic shutoff keeps engaging.
Of course, another reason is that it's wasting gas. Why allow gas to spill out with the price that it is?