I agree, the only thing governments should be doing is providing essential services to the public like universal healthcare. It should not be used as a system of control.
The government shouldn't be used as a system of control, so it should control the healthcare system. Flawless logic.
Universal Healthcare isn't about controlling the healthcare system. It's about providing healthcare to everyone who needs it and makes sure the workers in it get properly compensated.
You don't control them, doctors and nurses provide the healthcare because they love medicine. The government just pays them to reward them for their valuable labor which is a right.