The USPS does not deliver mail to every household. Nor do they deliver universally six days a week.
Where I live, USPS doesn't deliver to any household, but UPS and FedEx do.
But that is beside the point. Any party that contracted with the USPS would be obligated to meet the terms of the contract.
You might be surprised at who lines up to deliver mail up the Adirondacks. One of the virtues of a free market is the amazing ingenuity of entrepreneurs to meet market demand in the most efficient ways. The free market provides the motivation for such ingenuity whereas non-profit single-player monopolies often don't.
But still this misses my interest in this discussion. I think there is an optimum balance for publicly-owned infrastructure and privately-owned service providers. But that balance is not always obvious and usually not stable. I think there is great benefit in continuous discussion of the pros and cons to monitor and adjust how we leverage the strengths of both sides of the equation.
I like the idea of "build more rail lines." But it takes more that four words to make this happen. If you are just trying to replace the pork of military spending, then perhaps the details don't matter. Just trade one corruption for another. Let the power brokers beat each other up clamoring for the money.
But if you're making such radical changes to the redistribution of wealth, why not have some thoughtful discussion that people can reference for the next 100s of years. Who are the Lockes and Keynes of 2021? I know they exist. Let's bring them out in public discussion.