How about this; We put Uncle Sam in a position to do the most good; while not being able to do the most damage (day to day operation and control of people's healthcare). Make the fed the ultimate stop-loss; they pay claims on individuals over $100,000 - to $250,000 (and index it to healthcare inflation biannually); private en ies cover everything up to that point - with subsidies for people who cannot afford that lower coverage. The payor's file claims with the govt. for claims over the stop/loss - the govt. reimburses the claim; but doesn't have to get involved directly with the processing - although, obviously, they must have an ability to audit.
Pass a regulation, not controlling prices; but making pricing by providers transparent (doctors/hospitals/labs); they must post their charges publicly; and must charge everyone the same price - whatever that might be (I cringe at this suggestion; but for reasons that are more complex than I want to explain - there are a lot of shenanigans that go on in contractual pricing that should be stopped).