Some will, many people will still go into the profession. Especially if the training was free, and we could offer living in the USA as a bonus. Medical professionals will still be paid more than most people, just not as much as now. I suppose the US could even draft doctors, and pay them the equivalent in military wages if we really needed them.
Outsourcing and H1Bs worked to worked to lower IT wages, and we still have plenty of IT workers.
I work with a lot of smart people. Whether a person is in medical school for 8 years, or working as a plumber for 8 years is no difference. It's still 8 years. Pilots put in a lot more time training, have a greater responsibility, and get paid a lot less.
Giving up the salary for 8 years is the major sacrifice, not the 8 years. Paying people while they are in medical school would solve that. A salary of $30K while in school, and a guaranteed $75K once you got out would still bring in many people to be a doctor. Once you remove the malpractice issue, it's easily do-able.
There is nothing special about doctors, any more than IT people, teachers, pilots, bankers, or even mechanics. All categories of people are smart enough to be Doctors. There are even people that went into business for themselves that would/could have been a doctor, but decided against it because of the limited availability of medical school.
Open up medical school to many more people, forgive student loans to those that commit to working for the government or government pricing, and providing disincentives to doctors that do not want to work with the payment plans.