Indeed, I think the deal should be: You go to medical school for free, then you work for the government for a nice professional salary. Malpractice insurance can be a government function.
An interesting side effect might be to change the demographics of who can become a doctor, maybe attracting more people from middle class or blue collar backgrounds.
As opposed to working for the insurance industry? My knee jerk response is that incentivizing the best and brightest has gotten us to where we're at now. I've read that doctors are deluged in paperwork and bureaucracy, and incentivized to choose treatment options based on insurance coverage. I've had more than one doctor say to me: "The insurance says I can do X but not Y," and "your treatment ends when your coverage runs out." Of the several doctors among my friends, those who are not also professors or entrepreneurs have opted for part-time status, or have retired early.
Incentivizing the best and brightest in the software industry has gotten us to where we have to give new computer science graduates a coding exam, to find out if they can program.
An interesting side effect might be to change the demographics of who can become a doctor, maybe attracting more people from middle class or blue collar backgrounds.