"Now what happens when those doctors are servants of the State? "
They already are if they are working with insurance companies, because they honor that insurance company before you and they model their practises and treatments around their guidelines and payment schedules. The State is also getting more insistent on mandating insurance companies along with the pharmaceutical companies, including your medical records. This is now extending into cursory "mandatory" vaccinations at the whim of the state run pharmaceutical companies.
We may not be able to sneeze in a couple of years without it going "on record".