This seems like a great idea. It ensures that even if government efficiency is low, it is providing positive value. I'm surprised this concept isn't more widespread.
But there's always the risk of a pathological co-dependency on government employment. You can see this in many developing countries. So for partly legitimate reasons, the Civil Service has long been the boogeyman of Republican politics. Specifically, that civil servants are reliable "big government", Democratic voters. Better to 1) pack their voting power and 2) prefer private out-sourcing. This is one major reason (if not the major reason) why government agency activity and policy have migrated to D.C., and why the headquarters of so many corporations have moved to the D.C. metro area.
Those that choose not to move can leverage their experience in private industry.