The problem is the medical educational system is very tightly self regulated, and has been for decades. Law schools are not. The result is every year we have law schools all over the country practically $h!tting out lawyers. There are far too many of them per capita compared to doctors. Because the medical profession only allows X number of students access to medical school each year. And even if they opened their doors to more students, the higher, longer, more difficult learning curve, along with the high washout rate, combined with long, exhausting internships, would result in far fewer graduates.
You can become a lawyer much easier, quicker, and cheaper than you can become a practicing physician. Add in even a much more expensive, difficult education to become a specialist practicing in all but endless fields of medicine, and few make it through. And if and when they do, they are faced with paying a staggering yearly malpractice insurance premium that most don't earn enough to pay for right out of the starting gate. New doctors pay far more than older, more experienced physicians with a clean track record in the profession. Much like a older driver who hasn't had an accident or a traffic ticket in 20 years, will pay much less than his teenage son who just received his drivers license.
None of this can be solved by passing legislation, let alone turning it over to the government. You can have most any ambulance chaser lawyer out there successfully defend you in a minor civil court matter. But when people are very sick, they want, "the best". And that market is so confined, most of these top tier specialists can charge whatever they want. When you look at everything that is creating all of this, it's all but impossible to "fix".