I have to agree that having this tax as a separate "voluntary" fee, with no way to opt out, is ridiculous. Doubly so in that it became an involuntary fee in 2013, when cord-cutting was well under way worldwide. It should be taken out of a general tax fund, and relevant taxes increased accordingly, given that there is no way to opt out. Another avenue would be to add a tax to the purchase of TV's, radios, and other devices capable of accessing the public broadcast content.
In the UK the reasoning for a TV Licence is that it doesn't make an income from advertising revenue. However in Germany there is advertising though limited. The case to remove licences would be for these stations to fund themselves through advertising. After all you need to pay a licence to watch a self funded TV station as well as a state funded one. Do we really need state funded media in a modern democracy?
We don't need state funded entertainment, but there is still a case to be made for the societal importance of state funded news, informational, and educational television.
Profit motive is largely incompatible with honesty and accuracy in informational media. Of the hundreds of supposed commercial news and "educational" channels, every single one if chock full of deliberate misinformation. For every truth, there are distortions that are more profitable. Commitment to accuracy has limited commercial value in a marketplace where there are so many distortions that consumers cannot actually tell who is being consistently accurate. Plus, most people do not want accurate information, but rather want confirmation of their beliefs. Yet, for the same reasons we have education requirements and publicly funded education, we need (and liberty cannot survive without) the public getting accurate info, whether their is profitable demand for it or not.
Of course, in fascist societies, state funded information is even worse. However, state funded informational media can be and usually is more honest, accurate, and less manipulative than commercial media, WHEN it is in a relatively open democracy that also includes largely unregulated commercial media.
The keys are that the programming is not directly controlled by political office holders, and their is commercial media to challenge authoritarian abuse and government misinformation. The irony is that while commercial media is very unlikely not be distorted for financial gain, its ability to expose obvious misinformation by state funded media, wind up making state funded media typically more honest and accurate than the commercial outlets.
That said, I think state run media should have to stick to non-fiction, non-entertainment, fact-based programming. They can be held accountable in that area. Fiction and entertainment is inherently rife with subjective values, political preferences, etc.. The state hiring people to decide what subjective values and ideologies they want promoted isn't something that is in the public's interests and is a stone's throw from propaganda. Any values that are universal enough to not be controversial are going to already be promoted in culture and present in commercial markets (the market works differently for values than factual information because consumers can know when they agree with a value but often cannot know when they are being misinformed).
Addendum: Even when state funded media is run by people with a bias, the bias tends to be qualitatively different than the effect of a profit motive bias. The worst situation is when all sources share a similar type of bias, because it makes it near impossible to detect when and how the bias is operating. If you don't have any unbiased sources, the next best thing are multiple sources with different types of biases, because this produces obvious differences in what they are saying when one or more of them is engaging in bias, which is at least an signal that you need to verify who if anyone is being honest.