Many of USPS' problems could be solved simply by raising prices. The USPS clearly wins business on the last mile service level, and it would open up new opportunity for others to deliver Amazon packages if prices went up.
One other little known fact about the USPS is they cut lucrative deals for big customers. Negotiated Rates (NSA) can allows companies such as Amazon to buy postage at a significant discount. These deals should be eliminated. Why should a poor person pay more for postage than Jeff Bezos to ship the same thing?
From left field this is one of my ideas: Post offices could be replaced by adopting a NinjaVan model. Why can't every corner store in San Francisco be a post office? It would be amazing.