The links I gave you were not all "right wing" talking points and a couple of them were full of scholarly statistical research.
The Cato Institute is a libertarian group:
http://en.wikipedia.org/wiki/Cato_Institute
You wrote: "when if it was done by the government it would be a simple uniform system for every claim"
Can you give me an example of any endeavor by the federal government that is not a bloated bureaucracy? Granted some of them might get the job done such as the military, but do you know how much waste there is in military spending.
Taking the price component out of any transaction including health care guarantees shortages. In 1979, the government fixed the price of gasoline resulting in long lines and shortages.