Luxembourg is expensive because of their tax laws, just like Switzerland and Liechtenstein. They attract some wealthy people. Cost of living seems higher because there's less taxation on wages and profits, compared to most other countries in Europe. That's compensated by tax on consumption, via VAT mostly.
The cost of living doesn't "seem higher," it simply IS higher. If these places attract wealthy people, then where do the people who do the actual work (plumbers, mechanics, electricians, construction workers, bartenders, wait staff, etc.) live?
But cost of living hasn't got much to do with cost of education. The education system in Luxembourg is comparable to the one in Belgium or France, both in effectiveness and cost.
Oh, really? Schools must be built on land. Land costs money. Materials for the construction must be purchased with all local costs and taxes incurred. Then the people who design and build the school must be paid enough to live in the country. Finally the teachers, principals, admin staff, maintenance staff, cafeteria staff, etc. must be paid a living wage. All of these things are dependent on the cost of living.
The fact that the money isn't spent wisely in the US, as you say, only makes it a lot worse. You're spending below average and not effectively, which explains a lot. It helps the top layer of society stay on top. An average working class kid can't get into Harvard, fi, unless he or she is way smarter than average. In that case, he or she is absorbed into the top layer.
That's what happens with too much top-down government interference in schools. Various Federal mandates from testing to food, to you name it, must be paid for whether the local district wants it or needs it or not. Elite schools rarely enroll average Americans. A few get in with excellent test scores and scholarships. Most don't need to attend such an expensive school to excel in life if they've got the fire inside. We already discussed that fact. "Absorbed into the top layer" is called social mobility and is a good thing. We don't have a caste system of some fixed class system here. Anyone can rise or fall based on the decisions they make, the risks they take, and their abilities.
The US attracts a lot of brain power from the rest of the world. Makes sense, as most of these immigrant PHDs have studied in a system that doesn't burden them with loans to pay back. But it's not fair at all on Americans, as they are burdoned with debt and have to face competition from everywhere. It's also not fair on the education system in developing countries, as a lot of their PHDs emigrate to countries like the US. I also see it as one of the reasons over one percent of US citizens leave the USA every year.
Yes, we do attract a lot of people from abroad. I'd prefer if we were more careful about apportioning H1B visas, frankly. But many students from abroad come here for graduate school and then elect to stay as citizens. So not everything you outline is accurate.
Finally, there is no way that 1% of US citizens emigrate annually. That would be at least 3.3M people. Estimates of the total ex-pat population range from 5-9M total (and some of those live abroad temporarily or seasonally). Far more immigrate here than emigrate away. Check your figures.
