Reducing the number of “touches” an order needs before it ships out the door reduces the complexity inherent in your fulfillment operation. And as complexity is removed, error goes down while speed and efficiency go up.
In most fields of engineering, complexity is the enemy. The more parts something has, the more chances there are for something to break down. The more an item is handled or taken apart, the more space there is for something to go wrong.
A similar principle is at work with any complex operation, including order fulfillment. Although no one step in fulfillment is complicated in itself, orchestrating the many steps, time and again, and ensuring their accuracy, can be a substantial task.