Tax money is not necessarily wasted. There are plenty of places where outsourcing the work is the economical thing to do. The question is whether or not in a particular case if the outsourcing contract is economical. A blanket argument that tax money shouldn't go to private individuals makes no sense in an economy that isn't completely nationalized, since the government quite literally doesn't do everything.

While I don't know the particulars of the Autobahn privatization controversy, I do know about toll booth and parking meter privatization in the United States, and yes, they tend to be bad deals for the tax payers, because the government wants a quick hit of money, in exchange for multiple times that money over the long term. Take for instance, Chicago's parking meter privatization, where the city got $1.15 billion in exchange for all the revenue from parking meters over the next 75 years In 2015, the meters brought in $156 million, so we're talking at least 7x.[0]

[0] http://chicago.suntimes.com/news/parking-meters-garages-took...