Back in the 1950's doctor's would make house calls, but since instituting Medicare and Medicaid, requiring Certificates of Need to build new hospitals, the explosion of lawsuits raisng doctor's insurance costs, and so on, the cost of seeing a licensed doctor has skyrocketed.
Blue Cross/Blue Shield is supposedly a not-for-profit insurance company, and I've read about co-operatives in the Mid-West that offer insurance, but it's not free, and not even that cheap. It seems that the only way to actually reduce costs is to get the state entirely out of the way, including it's licensing of doctors and other health professionals, and letting people decide for themselves who they want to see for care. This would offer the greatest number of choices for everyone.
Instead of all doctors and nurses requiring long-term studies of all aspects of medicine, people would have the choice to see specialists, as Jawn Disease said. One specialist might only have experience in x-raying and treating broken bones and sprains, for example, A person might turn to him or her if they fell fell and suspected that they broke their elbow. Or, an experienced nursing assistant could build up a general practice wtihout a medical degree, but might refer a person with chronic, untreatable, headaches to a brain specialist, who might then refer them, if necessary, to a brain surgeon with an advanced medical degree. Anarchists want less authoritarian state intrusion in their sex lives, in how they build their houses, and in everything else, including health issues. In Ecuador, among other places, people are treated like free adults, and don't need to see licensed doctors for prescription drugs. They can buy anything they want over the counter, and can ask a druggist, or whoever they want to, about what to use and how to use it.
In the meantime, while the state still rules, it makes sense for anarchists to accept every grant and every benefit the state provides, including medical care, while at the same time hoping that it goes broke so it doesn't have to be smashed by force.