Wow, you have an example of propping up a government monopoly from 1851. Got anything more relevant to the world we live in today?
A big part of "Letter Mail Co"'s success was that it only offered services in the most lucrative of markets - a few large cities on the East Coast, whereas US Post is obliged to offer delivery for the same stamp price throughout the country. Letter Mail Co driving US Post out of business in those big cities would drive prices up everywhere else. See how they'd go if they were forced to build and staff their own post offices in every village, town and city across the country.
And of course, any profit by a publicly owned company replaces taxes. A drop in revenue could lead to taxes rising, a hidden cost in privatizing a service. Look at Singapore, 14% tax, 60% Government ownership. They could privatize everything, but taxes would have to rise to compensate.
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People being educated pays dividends for more than just the person with kids. Business's take for granted that they'll have literate 18 year olds to hire for minimum wage.
If you think literacy is bad in the United States, one of the countries with the highest literacy in the world, due in no small part to public education, think about living in a country with poor public school access, where literacy is 49% rather than 99%
Everyone benefits from education, even if you're not the direct person being educated.