Even the military isn’t THAT efficient. Take a look at military hospitals sometime.
And for a view of the future of healthcare under the auspices of the gub’mint, look at a Veteran’s Hospital...
Neither are private businesses. Again, the central driving point that I am trying to make is that there are a priori reasons for and against government intervention on various issues, and the matter ultimately is an empirical issue. Europe's economic woes are generally a strong testimony to the fact that the private solutions are better. But health care is an exception.