If the nation has socialized health care, it's possible that there will be some very attractive grants for qualified students to attend medical school.
ummm, if we socialized health care, we would be paying for health care as a nation, so I imagine all those people who need to have emergency care but can't afford won't stick the doctors and hospitals with the bill anymore.
Those poor doctors... actually getting PAID for their work.
The demand for doctors will increase as well, due to the aging of baby boomers and the treatment of the uninsured and plus, its not like insurance premiums are done with. Only a small fraction of Americans will be on a government healthcare plan. The majority will be in the private sector. With the need for more doctors comes higher pay, as an incentive to attract more people. So the loss of pay will largely be offset by the increasing demand.
Because people will still want to become doctors, and help save lives, and make lots of money, and have "status" and "prestige".
Why would that change simply because a different entity will guarantee insurance for poor people? There's no logic in your question.