Broadcasting, as opposed to the 100% Nazi party controll of media before, was thus setup to be independetly funded and run. The ZDF, if memory serves well, is allowed to be more of a government policy outlet than the ARD and the third programms. The goal is to prevent media to become government controlled, with the added benefit of being independent from add revenue. And that principal is still pretty solid.
This was the original intent: Adenauer wanted a federal public broadcaster to compete with ARD which he considered too critical of his government. The constitutional court shut that down as only the states have the right to set up public broadcasters with domestic transmissions (Deutsche Welle is focused externally). Today ZDF and ARD have the same legal framework, they are just organized differently.
The latter has been the status quo in Germany for the better part of time since WW2, and arguably people were less radicalized on both sides of the political spectrum than now.
It is when institutions get overtly greedy that people start to complain.
It is protection money: You haven't ordered any service and if you don't pay they'll make you pay and ruin your credit score in the process.
In the collection process they pretend to be a government institution to avoid going through local courts, which sometimes are against them.
EDIT: Also, I'm beginning to wonder why any criticism of the German government or especially state TV is being downvoted here. Civil servants have a lot of time ...