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.