The whole campaign against the TSA is idiotic and it is entirely based on some people's nefarious plans to replace the TSA at various airports with private companies that will be able to extract monopoly fees from airlines and passengers. Let's not confuse the two issues.
https://en.wikipedia.org/wiki/Screening_Partnership_Program
And in any event, the security theater will remain as cover and a scapegoat for politicians, airports, and airlines in the [inevitable] case of a security breech.
That said, the screening at San Francisco International is managed by a private company and they do a pretty good job, avoiding many of the really stupid problems exposed at airports elsewhere. It's still security theater, but done relatively competently.
More importantly, it transfers liability for failures from airlines to the public, which is the major reason the function was nationalized.
It has not been prove to do anything. That's not the same as being proven to do nothing.