From what I've read, doctors are also substantial owners of the malpractice insurance companies. Also, their premiums are paid by their employers. In fact, salaries don't tell the entire story for doctors, since they are heavily invested in their own industry. For instance, at one point my health insurance provider advertised itself as being doctor-owned.

As mentioned above, a problem is that the system is so opaque, seemingly by design. A potential benefit of a government run system is that there could simply be fewer business entities. For instance, doctors could just work for the government, for a decent salary.