I bet you that Netflix is one of the largest customers the USPS has, if not THE biggest.
Netflix says they ship over a million discs each day, so divide that by 35,000 titles, and you get an average of 28 copies of each title. It's more likely that they have hundreds of copies of some titles, and only one or two of others.
This figure also means that an average of 77% of their inventory is rented each day, leaving each distribution center nearly empty at the end of the day.
A million shipments each day, divided by 35 distribution centers, means an average distribution center ships about 28,000 discs each day. I know that Sunnyvale, CA ships 100,000 per day, so that means there are some facilities that ship far fewer. Still, imagine how big a truck you would need to hold that many.