Primary education is "universal" and "socialized" in the U.S. and yet we still spend far more than other nations while still getting worse results. Plus without recognizing any of the benefits to scale or "fewer middlemen" than you're claiming. Hell, the amount of administration personnel vs. teachers has exploded over the years making the costs even higher than before.
So please explain why U.S. healthcare would provide all these claimed benefits if universalized/socialized when direct experience shows the exact opposite with education?
You have a very good point. The big difference is that medical treatment is a realistically attainable goal. Doctors really can provide effective treatment.
In contrast, trying to take kids who have awful parentage and no interest in education and transforming them into college-ready high school graduates is a much more daunting and often impossible task. On top of that, our public schools are supposed to indoctrinate them with mamby-pamby political correctness, so they have to be taught to value and respect other cultures, to be nice to women, and to not use the N-word, etc, and we're throwing gobs of money at it.
In short, the reason why our education system is failing and costing us tons of money is because our society is trying to attain impossible goals. We're trying to take people who are mentally cut out to be ditch diggers and turn them into college-ready high school graduates. We're trying to increase people's IQ's and g-factors, essentially change their genetic makeup and brain structure though public education, and it simply can't be done.
Americans are using education as a proxy for solving economic and social problems -- if only everyone had a college degree all of our problems would magically disappear, including racial inequality, etc.
So American society is trying to educate kids at seemingly almost all costs to attain those goals.
Fortunately, the goals of medical care are attainable. It's not that amazingly difficult to fix a broken arm or to diagnose an infection and prescribe antibiotics or to remove a gallbladder. In contrast, if the goal were to provide Americans with immortality at any cost or to make sure that no one ever drowns or dies in a car accident, then it would be expensive and unworkable, just like our education policy.