Not to mention, they are required to prefund pensions for their employees, something no other entity is required to do. They also are required to take a letter from anywhere in the country, and deliver it to anywhere else in the country, within a couple days, for less than 50 cents.
The USPS' profit margin is aggressively controlled by Congress, which makes sense considering that they're a Constitutionally mandated monopoly. However, it also means the Republicans can inflict their "starve the beast" strategy on it at will.
"Economists regard seigniorage as a form of inflation tax, redistributing real resources to the currency issuer. Issuing new currency, rather than collecting taxes paid out of the existing money stock, is then considered in effect a tax that falls on those who hold the existing currency.[4] Inflation of the money supply in the long run may cause—and, all other things being equal, will cause—a general rise in prices due to the reduced purchasing power of the currency."
The problem is the amount. Going by this page[1], there's a net production of less than 30 million dollars per day. Let's round up to 11 billion per year. The M2 estimate[2] of US money supply is 13495 billion dollars. That's a seigniorage tax of less than a tenth of a percent per year. It's also less than a tenth of a percent of US GDP alone.