My Amazon packages are delivered almost exclusively by Amazon trucks and contracted delivery vehicles; the only time I see USPS used is when the package is tiny and/or it is a 3rd party seller not using Prime.
I know my situation doesn't apply everywhere, but they are trying to create their own delivery system and it works pretty well in my area.
They probably use USPS for last-mile in smaller cities and rural areas.
The real solution is to let people in more remote areas foot the increased costs of delivery to said areas. Pay for what you use.
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