Those links don’t say what you think they say. Or your definition of free market capitalism does not match up with what most people think or the OP was saying. Is that it? Or am I wrong?
That you linked some of the more progressive countries in the world to make a case against OP makes this all disingenuous. I agree that there are market solutions to health care and education but the examples you give are not exactly “free market”, not the way many Americans define it (not in general discourse). These are highly regulated systems that have set standards and subsidies and regulations. Schools in the link, for example could only be run by non-profits. Vouchers were equal for all students (again with subsidies) and actually worth something (whereas all current voucher programs are too little).
With health care individual mandates are required and other forms of non-libertarian government meddling. From talking to doctors here, the main point is some aspects of our system must change (how we pay procedures more than outcome etc), and that doesn’t happen overnight, to be fair.
Really interesting reading, and maybe you were trying to say there is more than one way to get to that level of social progress? If so I know I agree but it means that the central premise of OPs article is true: you still need the government to spend and to pay into such a system. To say nothing of the regulation needed. This is a far cry from libertarianism as normally defined. 
 and I won’t even get into the many other social programs those places have to help alleviate the health care system or that helps with education.