There is little privatization in the U.S. in the areas I mentioned. For example, less than 10% of Americans go to private or charter schools. In Denmark, Japan, Spain, Korea, and the Netherlands, that number ranges from 20-65%. Few American roads are privately-operated (mostly some turnpikes). In contrast, all of the French autoroute (highway) system is private. Much of Japan's highway and transit system is private too.
Transit is almost entirely publicly owned and operated in the U.S. For example, Amtrak is both owned and operated by the government. In contrast, Deutsche Bahn and Eurostar are are private companies (though subsidized by the government). SNCF, though owned by the government, is run like a private company. E.g. in contrast to Amtrak, where only a single route produces an operating profit, 80% of SNCF's routes produce an operating profit. Japan's key railroads are privatized, and the biggest one (JR East) receives no public subsidy.
Anti-development housing policies that drive up prices are all done by the government (compare to Japan's lax zoning laws).
Healthcare is really the only thing that's more privatized in the U.S. versus other OECD countries, though it's less than you might think. About 50% of healthcare spending in the U.S. comes from direct public money, comparable to Korea, versus 70% in Canada or Spain, and 75-85% in Italy, Germany, France, and the U.K. However, if you account for indirect expenditures (public subsidies for health insurance), the total comes to about 65%, not much less than in Canada or Spain: http://www.pnhp.org/news/2016/january/government-funds-nearl....