Education is not an externality, and should be handled by the free market, not the government. Public education is in a horrible state everywhere you go, precisely because it’s public.
To commit to private-only education would result in a country with a very large section of the population uneducated. It's also a massive waste of human potential. Sources? Most of pre-20th-Century Europe, and much of the less developed world.
So you'd either move around them or pay them enough. It'd be significantly more costly, but "impossible" seems like a stretch.
I'm not saying it'd be better, mind you; one can still be a staunch believer in the importance of the State. But to claim that the human species would stop transporting stuff if eminent domain was unavailable sounds to me as lack of imagination.
So spot on about railways example: the real problem to solve is transportation, not railways, and a different form of transport could replace railroads.
So spot off about education: it damn is an externality! Try living in two societies/regions with different average levels of education and see how it feels. Also try starting different kinds of businesses in places where the pople are on average more or less educated. Also try implementing things like pollution reduction strategies or crime fighting strategies for places/communities with varying levels of education!
Yeah, it does not always work in the most obvious ways: a college educated person will not always make a better decision than someone who dropped out of high school. But the high school dropout from an on-average well educated society will most of the time be more of a person you want to be around with / sell to / buy from / live on the same planet with, than anyone from a less educated one.
Replace "educated" with "science literate" for the clearest particularization of what I've just said, as other types of education have more variability in effects on people and are easier to "get wrong".
What’s the correlation between crime fighting and education levels? What you seem to be suggesting is that people need to go through some sort of a brain-washing process in public schooling to be good members of society, which is scary.
1. Railways are a real and concrete example of wrongheaded privatisation.
2. More congested roads are not an alternative to efficient rail services.
3. The greatest technological innovations of our time from cancer drugs to satellites to the internet are spin-offs from government funded research. I could bore on all day about this...
4. A good education system is an externality in that society as a whole benefits from highly trained doctors, engineers and even in my view artists and poets. It is a profoundly social enterprise that we all have a stake in.
5. Public education maybe messed up in the US (I don't know it well) but it's doing just fine through much of Europe and the UK - or even in profoundly free market economies like Singapore. Indeed the UK in particular where the tensions in education exist over school placement and better/worse schools within the public system illustrate that educational variation is usually down to social status and economics - not public ownership.
Of course. The rich use the State to publicly fund research (socialize losses) which they then commercialize and profit from. Otherwise they'd have to actually pay for the research themselves.