In Australia and New Zealand we have good public health systems although far from perfect and you are right about the politics. Most of Western Europe seem to have excellent systems. Look at the trouble Obama has has introducing a fairer public health system in the USA.
I have observed over the years that one of the hardest jobs for a minister in government is governing Health. However I have known excellent health ministers with real vision who under their governance can achieve fantastic improvements in health care.
In my opinion an effective health system private enterprise can never be the main player. A business model for core health services doesn't work - Effective and fair Health services where everyone has access to will always be a liability. Care costs more than the profits that can be made. If you look at the World Health Organisation statistics on the countries that enjoy the best health that is spread across the whole population- without exception all countries have sound public health systems and many of the top countries have almost exclusive public health systems.
That doesn't mean private health care doesn't have a role. Many countries have very good partnerships between public and private providers. However the countries in the world that have fair equitable and effective health care all have at least core services that are provided by the public purse.
I suppose I will be accused of being a red :=(