> When it comes to delivering first-class mail for cheap, I assume there’s a minimum population density that allows for such a thing to be done cheaply (similar to now) and profitably.
This is a bold assumption that needs backing, because it would suggest that Germans or Britons would be paying 2 orders of magnitude more on sending paper mail than Singaporeans. It also presupposes that private corporations must absolutely turn a profit on every piece of mail that they deliver to every destination, but that’s not how most enterprises work — there can be sustainable loss leaders. It also presupposes that we ought to subsidize rural paper mail delivery rather than charge the true price, which is also debatable.
> I’d bet there’s a threshold somewhere in that range where it wouldn’t be possible to deliver a mail anywhere in the US by a private company for similar rates that everyone currently enjoys now.
“I’d bet there’s a threshold”, how do you know that the US isn’t above that threshold?
> equitable pricing
This is also debatable, because the USPS is essentially charging higher rates in denser markets to offset the subsidized rates in sparser markets, which imposes a regressive price increase on poor urban USPS customers. Higher prices mean nothing to rich people. If there’s some social utility to having rural (and not urban) Americans enjoy subsidized first class mail, then why not just subsidize it directly through taxes as opposed to selective price increases, which can be regressive and un-equitable?
> Not every damn thing needs to be privatized, some things are better left as government entities because the benefit to the public is greater than any profit motive. Letter delivery is one of those things.
Is food one of those things? How about clothing and shelter? The profit motive is just an incentive for private entities to provide goods & services. The strongest argument in favor of the profit motive is that resource allocation is superior among private entities relative to government central planning. There are obviously exceptions, like externalities, but those don’t really apply here.
And even if we did decide that there’s a public benefit to providing subsidized mail to rural areas, that’s an excellent argument in favor of keeping a taxpayer subsidized USPS, but not a sufficient one in favor of maintaining its monopoly on paper mail. Especially considering that private corporations already deliver packages to low density rural areas alongside USPS just fine.