Can you summarize what his argument is? Can't we count on some upfront testing that will weed out the people who clearly cannot call themselves doctors? Is testing the same as licensure?
The rebuttal would be "Fine, but certainly state licensure can't hurt. It's just a backup." He says that it does in fact hurt, by allowing the AMA to control the supply of people who get to practice medicine. This limits patients' options w/r/t how, from whom, and for what price they can get medical care.
E.g. suppose I find a competent, well-trained nurse to remove a mole for me. The nurse and I agree to go ahead for $100. Friedman says that it's a) morally wrong and b) inefficient for the government to barge in and say, "No, for your own safety, you're not allowed to make this voluntary agreement. You have to have a doctor do this. Oh, and it'll cost $300." That's the effect of a law that says only licensed physicians are allowed to remove moles.
We have much the same situation with examinations boards for school leavers in the UK. A competitive market for examinations providers and schools incentivised to maximise pass rates has unsurprisingly led to grade inflation as each board tries to 'best serve their customers'....