Realistically this is only because our private sector in that area is incredibly broken, not because the government is doing an incredible job.
There’s many other comparisons where the government comes out ahead when you balance quality of what’s done vs cost. The overhead of the social security administration is far lower than other pensions, and that’s with everyone else piggybacking backing off your SSN. Some of this is scale but economies of scale only go so far.
It took me a while to realize there’s just less money to be made when the system actually works.