Singapore, I think, has the closest thing to the sort of system Hayek had in mind. Among wealthy countries, it spends the smallest percentage of GDP on health care, and it gets about the best results. You know what that’s called? Efficiency. How do you get it? Competitive markets with freely moving prices under the rule of law! It’s the sort of thing you’re in favor of if you want everybody to have access to really good health care and money to spend on things other than health care.
I'm not a big Wilkinson fan, but this post on why no one should be confused in to thinking Obamacare is something Hayek would support is right on the money.