This isn't even close to true. Keep in mind that Medicare, together with Medicaid (which operates under much of the same administrative rules), account for nearly half of medical spending. So basically, if a provider doesn't want to play by their rules, they MUST deal with Medicare. That is, the government is nearly a monopsony in this industry.
There's a common, misleading, claim that Medicare is more efficient because they spend far less than commercial insurance on overhead like claims processing. This claim is true. But the impression that it gives is absolutely the opposite of reality. The reason that Medicare doesn't spend as much on admin is that they offload all of this work onto the providers. Every hospital in America has a "Medicare Reimbursement" team. A moderate-sized hospital is going to have something like 2 FTEs focusing just on the reimbursements from Medicare and Medicaid. And that's a lot more work than just filing the right forms for each case. There's a ton of additional work. Each spring they have to file a HUGE "Medicare Cost Report", requiring a couple of months of work to get all the data in place for it. (Source: my wife was "Director of Reimbursement" at various hospitals for quite a few years, before going into consulting.)
That Medicare Cost Report that I mentioned is, beyond a huge effort sink, the source of many other evils. Because of the amount of work that's needed to gather and collate all this data, hospitals naturally structure their Accounting around the way Medicare wants them to report. The thing is, that's largely orthogonal to the way a rational person would do cost accounting. The result is the common criticism about how widely varying the cost of a given specific line-item is between hospitals: they don't really know how much a given procedure costs because that's not how they track their expenses, so they apply some allocation heuristics, and every hospital does that a bit differently.
There are also various perverse incentives in the system. For example, Medicare is smart enough to know that it costs more to deliver care in NYC or SF and so forth. Every locale has a Cost Index that scales how much they expect to need to pay. This leads to hospitals needing to show that their expenses are higher so they should be classified into locale X rather than neighboring locale Y.
Another one my wife told me about her hospital: Medicare realized that a lot of UTIs were hospital-acquired, and they rationally said that they would no longer pay for UTI treatments unless the hospital could prove that they were not hospital acquired. Well, maybe that wasn't rational, because with Medicare/caid being such a huge portion of their business, they changed their policy to test for UTI for everyone at admission, so that they could furnish the proof demanded. Think of all that wasted lab work...
So no, Medicare is NOT more streamlined and efficient. It's absolutely, 180-degrees, the opposite of that.