Governments add far less overhead in this area because they have more data and can thus use random inspection of bills for validation. Further, when setting rates every insurer has a separate negotiation involving even more overhead.
The government hires health insurance companies to do the inspections. I don't know of any US government that doesn't contract implementation of Medicaid/Medicare to UHG/Anthem/Humana/etc. So all the insurers have all the data anyway, and they are not inspecting each and every bill, they are also using heuristics.
Using heuristics on smaller sample sizes is inherently less efficient. You can get reasonable polling data on 50 million voters using 10,000 samples. That’s 1 sample per 5,000 voters. Drop the election down to a local election with 10,000 voters and the same ratio provides 2 samples telling you almost nothing.
Thus, if 5 insurance companies send patients to the same doctor you simply have more overhead.
