I don't think Amazon is trying to grow to ship mail. They want to grow to deliver their own stuff and protect their brand name. Maybe they would go after some of the postal contract to fill unused lift, but I don't think they will have any unused lift until they are much bigger than UPS and FedEx combined.

They could easily buy FedEx, but if they did so, it would be to protect their own business, not take on ours.

Just another opinion, worth what you paid for it.