Practically speaking, USPS does a lot of last mile package delivery that no one else wants to do, including Amazon. If USPS wasn't delivering to those locations no one would be. And we're not talking middle-of-no-where-Wyoming locations, plenty of places east of the Mississippi have only USPS too.

There's all sorts of philosophical arguments as well: government services shouldn't need to turn a profit, all citizens need to be able to interact with the State and the post office provides a way to do that, mail-in voting, Post Offices can offer stuff like general delivery for those without permanent addresses, etc.