It depends on what you include in healthcare costs but I will take issue with you on that point. Litigation costs can be dramatically reduced. Having standarized policies, as with Medigap plans, dramatically reduces costs in two ways. First it makes a medical insurance policy a commodity item. You know you are getting exactly the same product regardless of the vendor you select. That reduces the amount spent on marketing since vendors have only two areas in which to compete; cost and customer service. The Medigap approach saves money in another way. Medicare determines whether a claim is covered or not. The insurance company no longer incurs the cost of staff to review claims and look for excuses to deny them. Medicare could save a lot if it could purchase by competitive bidding. If you can do things more efficiently you can save money.
I do agree with you that there is no complelling evidence at all that the current proposal will do so.