Much like AWS spun out of their in-house experience running flexible computing infrastructure, this would be a natural fit for them to flex their logistics strengths.
Via their multi-channel fulfillment offerings, you can already use Amazon's logistics network to ship your products sold on or off of Amazon. This would just be supporting more type of shipments than just fulfillment.
On the other hand, Fedex, DHL, UPS etc have built a big part of their strengths of shipping worldwide overnight. That's very different than what Amazon does, where they try to warehouse products close to customers to minimize shipping distance and time. Great when you want to buy an iPhone, but not suitable for shipping a document from New York City to Tokyo.