New technology is not always better, and patients have no way of telling if it is. Doctors often don't know because the evidence for or against the new procedure/test is not out yet.

For-profit healthcare does not maximize health, it maximizes profit at the expense of patients and the rest of the economy. This is because preventive care is cheaper, and less profitable, but better at promoting better health. Your argument totally neglects the importance of preventive care, much like American healthcare.

It also neglects the fact that healthcare is different from other areas of the economy. This is because doctors are the ones who tell patients what they need, and a sick/dying patient is in no position to dispute whatever the doctor dictates. How much are they or society willing to pay for their life? Whatever it takes. While doctors may be more virtuous than the average person, they are not immune to pressures for more profit at the expense of health. Surgeries, medications, and many tests come with risks and complications and thus their inappropriate use is both dangerous and inefficient. On the insurance side, for-profit HMOs also undertreat people in the quest to save money with dubious practices like capitation. A single-payer government system could ameliorate this conflict of interest between health and profit, as well as promote preventive care to save money for the wider society, promote evidence-based medicine rather than rely on biased industry studies, and many other benefits that would improve the quality of, access to, and simplicity of healthcare.