We hardly ever have cut-and-dry systems in the world. Health care is a combination of capitalism and socialism, its not purely one or the other. A purely capitalistic system would not prescribe unnecessary tests because people who did not want them or could not afford them would not buy them and doctors or hospitals would not make money from them. Sure, those who could afford them might buy them, but if they get no benefit from them (like three test results coming back negative), they may not buy them again at a later visit.
I agree that costs may be controlled when patients have ready access to health care, but it only works if those patients willfully access the care, which is another topic altogether. Because this country is made of individuals and its laws are written as individual protections, the public perspective is irrelevant. Taking a "public perspective" implicitly means that one person knows what is better for the person in question than the person in question does. That robs the person in question of his personal liberty to live as he sees fit.
I like what Spider said about for-profit companies. I know he was sounding a bit contemptuous of their dealings, but that is the essence of business in a free world. GM doesn't make cars because they like cars -- they make them so they can sell them and make money to put food on the table. Doctors don't pracitce medicine solely because they like helping people -- they also do it so they can put food on the table. It's not a bad thing at all. Those with the most money are usually the best at what they do. Don't fear profit -- it is merely a motivator to do better (which is why government is inefficient -- it can not profit, so it has no motivation to improve).