This made sense back when the 'statement' was actually a copy of the customer's ledger card and payments were posted to the card. Today, inquiries in the system tie all this information together. The packing list can be filed in Receiving and the vendor invoice can be filed in Payables. The new software release also has a Purchase Order reprint function, so you won't need to keep file copies. Most people find it helpful to get a fresh viewpoint by bringing in an objective third party to take a look at things.
Many companies find that streamlined procedures can save enough money to pay for the consulting.