The ARD and ZDF channels are not government funded in germany. It's a fee that gets collected by a dedicated agency, but not a tax. The System has its own set of issues, but in general I think the system is a good idea.
For the consumer it certainly looks like that. However, the legal underpinnings are completely different with all sorts of interesting side effects. The basic idea was after WW2 that the radio should be as independent from the government as possible, so a completely separate system of funding was set up. The government has no say in the way the money gets collected or spent and very little ways of influencing how much money gets collected. Now there are some checks and balances and ways how the politicians can actually influence the radio stations, but not via "we'll cut your funding if you don't report what we want."
The system certainly has its flaws and room for improvement, but a purely privately owned system is not a better option.
Oh, I know the background. But the leadership of the public broadcasters is full of party people, so it's not too different from the government in terms of who are the people in charge.