Public services are also required when providing a service to service level expectations wouldn't be profitable otherwise. We expect and demand that the post office deliver to every remote outpost in the country for whom there is no alternative, regardless of expense. Those deliveries could be anything, including something like medication. If you privatize it, a private company would immediately and naturally cut loose those unprofitable routes.

So in that way, it is an awful lot like healthcare. If you consider postal service a right, then it's functionally no different.