> Is Amazon going to run ships around the Great Lakes to deliver mail to vessels moving between ports?
No, because using planes to deliver to regional distribution centers is much more efficient.
> Is FedEx going to send a truck an a four-hour round-trip to deliver a single letter to someone on an indian reservation for 50¢?
The USPS does not deliver mail directly to the majority of reservation residents. Most have to fetch their mail at the closest office, which could be upwards of 1 hr away from them. This is because most reservation residences don't actually have an address (which also prevents them from registering to vote, which is another related issue).
> Is UPS going to charter bush planes to deliver mail to remote outposts in Alaska, Samoa, Guam, and the Northern Mariana Islands?
The USPS doesn't either. The USPS's Alaska Bypass has a minimum order weight of 1000 lbs, it's designed for retailers. The USPS does not serve normal consumers in very rural areas with standard mail features.