Given the trends of the capitalist US government, which constantly cedes more and more power to the private sector, especially google and apple, I assume we'll end up with a state-run model infrastructure as soon as we replace the government with Google, at which point Gemini simply becomes state infrastructure.
That's not correct. If USPS makes more revenue than their expenses for a year, they can't pay it out as profits to anyone.
It's true that USPS is intended to be self-funded, covering it's costs through postage and services sold, and not tax revunue. That doesn't mean there's profit anywhere.
Pricing in the US postal system is not based on maximizing profit. Ths US postal system is not a for-profit system, at all. It is a delivery system (more or less) that happened to start turning a profit (2006) until PAEA. After that, the next time it made a profit was 2025.
That depends on the country in question :-)