First of all, Medicare is only “more efficient” on account of price controls. “Legal inability to negotiate pharmaceutical prices” is just a euphemism for “inability to force pharmaceuticals to charge anything other than a defined amount of money”, or in other words: price controls. If a law was passed today that forced private insurers to use the Medicare fee schedules, they would be just as “efficient”. Whether price controls are an efficient way to run an industry is a separate issue entirely.
Second of all, Medicare is separated into “original Medicare” (which is the government-run insurance program), and “Medicare Advantage aka Medicare Part C” (which is private insurance offered to Medicare beneficiaries). The data we have right now shows that Medicare Advantage is actually the part of Medicare that’s working the best in terms of raw efficiency and outcomes[1]. 34% of Medicare beneficiaries have elected Medicare Advantage instead of “Original Medicare”, and that number has been growing[2].
[1] https://freopp.org/medicare-advantage-a-platform-for-afforda...
[2] https://www.kff.org/medicare/fact-sheet/medicare-advantage/