Both of these sentences are factually wrong. There is no government news in Germany. And the Öffentlich-rechtlich (which program is, again, not controlled by the government) are not really expensive (The price is 17,50 for everything together: TV programs, radio programs, internet presence).
Please stop spreading misinformation. The Federal Constitutional Court decided in 2014 that no more than a third of the members of each Rundfunkrat can be chosen by the state or by parties. Also, not all party representatives are representatives of a governing party. The ZDF Fernsehrat has representatives of each party present in the Bundestag. Two thirds belong to other groups such as churches and unions.
For the state-level Rundfunkrats, the federal government is obviously irrelevant.
There is not one single way to publicly fund media. Hell you could just leave the whole system as is as provide no strings attached grants or tax credits to all publishers. The point is, there is no technical solution to this, we need policy change.