Correct. "Collective bargaining" against society is called running a cartel. Having your cartel lobby the government to set the law to benefit it is called rent-seeking. They've caused massive damage to society, and limiting positions by quota is different from setting standards.

I can't even draw an "imagine if we limited... " comparison because limiting access to doctors is already close to the worst case, obviously destructive thing to do. Maybe food? If instead of subsidizing farming to ensure we always overgrow and don't have famines, we capped farming, ensuring famines?

Yes there need to be solidarity between members of unions otherwise it is just some feudal guild society.