You need to explain how you rank it as the best measure; is it total cost? is it the rich pay the cost for the poor (equity argument)? is it the prevention of fraud? is it the best delivered healthcare to people? Is it the minimization of waste and deadweight costs? I believe the metrics to evaluate what is best are complex and difficult to explain. That and you will have winners and losers in the process of adoption of universal health insurance. Politicians are not know to take risks in promoting policy.
Eliminating and minimizing the social risk (poverty, illness, aging) of human living is definitely an economic and financial issue. Maintaining a capitalist welfare system is economically and financially possible; a healthcare system can only be built up by starting a chain of payments and services, e.g. the healthcare for coal miners in Europe was started by labor organizations ('seed money') in the Middle Ages, in co-operation with willing physicians. Consequently, the current trend of profiteering, even from disease, is definitely an unhealthy practice by putting physicians under monetary pressure. Your economic question burns down to an ethical issue, i.e. the 'price' and value of human life. The medical sector can be organized as a non-profit enterprise; it is foremost a moral matter of collective value decisions.
Another consideration when contemplating the implementation of a universal health care system is the impact on health care delivery. That is, governments who operate the health care system have an incentive to save money on the healthcare budget. This results in reduced funding for healthcare. Other ways to reduce healthcare costs are to set up gatekeeper systems like needing to have a referral from your GP to see a specialist. This creates delays in receiving healthcare to patients. Also, reducing the number of specialists (high cost versus nurses, and GPs) saves money. Substituting nurse practioners and physician assistants (lesser quality) is another way. Medical treatments changes, for example, a higher use of drugs to treat patients as this is cheaper than surgery, et cetera. For the older population the government decides that some procedures will not be administered past a certain age. Initially the age might be high like 90 years old for hip replacement operations but over time that is lowered to age 85, then 80, next 75. Delaying or eliminating treatments saves money but what about the quality of life for patients and also the ability to save the life with early medical prevention. Even treatment of cancer is delayed which can have a great effect on mortality and morbidity. Illustrations of these factors can be found by looking at the UK and Canada universal health care systems.