That doesn’t work. Doctors specialize in specific things. There are probably doctors who legitimately have 100% vaccine exempt patients for medical reasons.
The real problem is that doctors can’t be “fired”. Stop asking the government to do something when it’s really the AMA licensing board that is the problem.
It’s a private organization that is run by doctors. Obviously doctors are not going to prioritize making it easier to take away someone’s license. Demand the AMA do something about “killer doctors” or something. If their brand is associated with sickness, then they might take action.