Why would your future Anarchist's Yellow Pages have the number of a heart surgeon?
Think about the implications of a stateless society: An individual needs to provide for himself and his own defense with certainty and celerity. That puts pressure on people to choose careers that begin to pay off as soon as possible. After all, the longer one is in school, the longer one has to rely on others for protection.
People would also feel pressure to choose careers that encapsulate skills they need to learn otherwise. Hunting, trapping, farming, carpentry, private security - these are things that a person can make money doing but also provide direct personal benefits.
So, in a system where a person has to be self-sufficient as quickly as possible, I don't see a lot of people signing up for the 12 years of primary and secondary education, 4 years of college, 4 years of medical school, 4 years of residency, and 2 years of fellowship necessary to become a Cardiologist. Even if society values Cardiology so highly that they'd give a qualified person a million dollars a year, the investment in years is still too high.
So, by the way, is the investment in money. Many people are only able to become doctors by borrowing over a hundred thousand dollars to finance their education. One of the reasons banks lend money is that they feel a certain security that they'll be repaid. And one of the reasons for that sense of security is that the banks trust that a foreign army won't just show up and shoot them, that criminals won't try to rob them, and that government services like courts and police will help them collect their money from delinquent payors.
Without a central government, banking becomes impossible. So does all long-term investment.
In an anarchy, there are no cardiologists.
I guess I need to use more smilies on posts like that. 
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