First benefit: about 20% of the cost of health care is the administrative cost of performing all of the billing and accounting procedures needed to satisfy Medicare and the thousands of insurance companies, all of which pay different amounts for every procedure.
Second benefit: The cost of what is being done for the patient again becomes a consideration. It isn't at this point in time.
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.
In a free society people should be free to contract for whatever services they wish.