I'm shooting from the hip here, but think of what we could achieve if we repurposed it. Think of those 574,000 employees, many of whom have direct knowledge of each household in an area. What else could they be doing if they weren't spending all their time carting mostly junk mail to people's doors?
Suppose we start freeing up resources for more needed tasks by only delivering physical mail two or three times a week. Half or a third of the delivery effort could surely be done with two-thirds or half of the people and vehicles, probably fewer in urban areas.
Rather than cutting jobs—in a time when more jobs are needed—shift those jobs into roles with more of a social return. Peace Corps is another independent agency of the United States; what if we started to shift the USPS infrastructure toward support of economic and social good here in the U.S.? What if we made a concerted domestic investment in increasing productivity and self-reliance in our communities?
I would sure rather have that than the ability for some person to carry a piece of paper from my house to somebody else's house in a couple days for less than 50 cents (as cool as that is).