As for free market health care and education: Are they really impossible, though? And if it's "purely" impossible, is it really impossible to introduce some fundamental free-market reforms, like school choice, or the ability to choose your own doctor?
As for "government-run education being successful" -- ever since I started school in the 1980s, government-run schools have been in crisis mode -- indeed, it's what's led to things like the Department of Education and No Child Left Behind. What's more, there is no evidence things are improving, and plenty of evidence that it's been degrading over time.
How many children's futures are you willing to cut off at the kneecaps until you finally admit that government education, particularly in the United States, has serious problems?