I think you do not have basic notions of economy. How can something be free? If it is free, it is because someone is doing the work (the doctors). If the doctors do not get paid a market price they are being exploited (forced to work for less). So that is where it is paid. You get it for free, yes, at the expense of those people that could have a better life and in the name of the good for everyone else they are converted into a simple tool for the propaganda of their leaders.
I wonder if that is ethical. I mean: forcing others to do a work that you consider good for the rest without giving them a chance for alternatives. Are those people worse than the people that deserve that health care? Should they be a means to a goal? There are two kinds of humans? The ones that are a means (doctors, rich people, etc.) and the ones that get benefits from them (the users or receivers of those things). No, I say no. Noone should be the means of anyone else. If we want something we ask for permission or cooperate. The rest is just propaganda.