There is indeed a housing shortage, or more specifically shortages in desirable metros. American cities are refusing to build denser residencies, driving up the cost of housing.

Most countries aren't America. Germany, as a point of comparison, had half the share of it's population enrolled in university. Part of this is because of age distribution: America is younger and has more college age people. Also, about 50% of German high schoolers go on to university as compared to 70% of Americans. People keep pointing to the European education system, but my retort is that following Europe's example would entail reducing enrollment considerably.

Healthcare is indeed one place where administrative changes could solve things. Most European countries, along with Japan and South Korea, work by giving citizens a stipend to spend on a healthcare plan from a marketplace of providers (either directly, or indirectly through subsidizing plans). This is largely what Romney was proposing in 2012, but that effort fizzled out. Unfortunately, the one party in America in favor of healthcare reform seems to be laser focused on a fully nationalized healthcare to the exclusion of anything else.