You keep using the word "unprofitable" to describe services that have a higher cost to provide. These things are premium services. Private companies are happy to provide them to anyone willing to pay their costs plus at least the market rate of return, precisely because doing that is profitable.
The example you're using is election mail. That's paid for by the government. How is it possible for the rate they'd have to pay in a competitive market with low margins to make it non-universal and yet it isn't already? If you want to deliver to everybody then you have to pay the cost to deliver to everybody, one way or the other. Subsidizing it through more expensive postage (disproportionately paid for by the poor) seems obviously worse than paying for it through taxes (disproportionately paid for by the wealthy).
The US government does not send election mail, because it does not conduct elections. Elections are conducted by state governments. Election mail should be a free service provided by the US government in exchange for states adopting certain mandates, such as universal voting by mail with no postage assessed to the voter.
