Orathaic, my concerns about its realism are entirely political, not practical. At least in health care, I think we could have a blended system. Catastrophic health care plans run by large national corporations (though, in a true free market, I believe we'd have far fewer of those, so I might be mistaken about this) would be relatively inexpensive, supplemented by mutual aid societies, professional organizations, and the like.
I also want to emphasize the difference between a free market society, a society which genuinely values free and fair competition of goods and services and ideas, with a merely capitalist or materialist one. A free market economy does not mean one in which all personal status is measured by wealth. The American Indians had a free market (but not capitalism) economy, and personal wealth for them was almost meaningless compared to the Western world today. It's all about values, including the values which shape the power and influence of the government. You might almost say I am advocating an anti-capitalist free market system.
Admittedly the years of government intervention in the economy have greatly warped public perception of things like poverty and charity, perhaps beyond recovery, but I am confident that a different system, free from the weighty hand of federal influence and less inclined to support the consumption ethos of international business, could succeed, at least in the United States. For one thing, America is so, so rich. I don't think people appreciate how rich America is because the wealth is so imbalanced, the government is such an expensive weight, and the culture is so materialistic (this last might sound counter-intuitive but I hope you understand -- we value the wrong kind of material wealth). But America is almost, or least could be, almost a post-scarcity society. Eliminate the varied government programs which promote the imbalance of wealth and promote a more local-oriented social outlook, and most communities could easily provide all of their members with food, clothing, health care, comfortable housing, and entertainment with less work than we currently engage in today.
Of course, we don't do that and most people don't think about that. Instead we live under a different kind of system, promoted by big business and backed up by the coercive power of the government's military and police powers. But we don't have to live the way we do.