What happened to them?
They were fired because of a law banning federal employees from striking. If doctors were allowed to negotiate with Medicare as a union, they would not be banned from striking and would not be federal employees.
Those who support universal healthcare often want a system where doctors ARE federal employees, like the British NHS.
What happened to the air traffic controllers? Some applied to be rehired and WERE rehired. Others changed their line of work. The air traffic controller ranks did not recover until TEN years later.
Look at the pilots union. An American Airlines captain can make $590k per year and work about 80 hours a month. They have limitations in hours so no need to take hospital call and stay up a night then have to see patients the next day. If they fly a red eye flight, they get to sleep upon arrival. A pilot often has a career of 43 years. A doctor rarely has a 40 year career. If the doctor retires at 65, they might have a career as short as 29 years if they went to medical school without any delay but did a cardiothoracic fellowship.
Basically a union can help members if the union leadership are not a bunch of lazy or corrupt fat cats. Individual doctors are at the mercy of Medicare, hoping that they will not get their heads cut off.