Third party payers are surely part of the problem, but isn't it easy to use more government force, as you are proposing, to "fix" the problem rather than stopping the circle of force?
In this scenerio, you would replace the people who force others to their solution, with yourself. To use force to make them use your solution.
Government caused the problem, it is not the remedy.
When it comes to medicine, there are few Americans who are not radical equalitarians. If that rich guy over there can afford a triple by-pass or a heart transplant, I darn well should be able to afford one too is the thinking
The problem is there is no possible way, even if we had a free market, for everyone or even a large segment of the population to afford all the high tech care available. And that means people will demand more and more government intervention. You and I will be taxed so people who cannot pay for a half a million dollar operation get one.
This is where the Libertarian Party always fails. The LP dogma goes nowhere when a society's deeply held moral convictions, in this case equal access to medical care, are in opposition to it.