In many cases the services that have recently been privatized were never nationalized to begin with - they were public services, like garbage collection or public transport, that have no obvious market competition model to follow.
Your definition of "rent-seeking" is also incorrect. Rent-seeking behaviour is when an economic agent attempts to manipulate public policy for private gain. A government body cannot engage in this behaviour by definition, as it does not take a profit, and is not private. It can fight its corner though - seeking more funding - but then it must spend that money on things like schoolbooks or hospital beds. This is considered a horrifying waste of resources to the private sector, which knows that those funds could better be spent on yachts and hookers.