Not saying I agree or disagree with your conclusion (I'm undecided), but I disagree with your reasoning. The question whether the Rundfunkbeitrag is good is partly philosophical ("what is the role of the state?") and partly practical ("does the state provide better media than private enterprise?"), and I don't think this example sheds light on either aspect.

This is also pure insanity: https://www.swrfernsehen.de/eisenbahn-romantik/index.html

They need to go to jail

Because you don't care for it?

I wouldn't say Musikantenstadl is just for old people. Perhaps 90% older viewers from what I can tell, but I can (personally!) guarantee that the figure isn't 100% ;)

Also, while I wouldn't watch it if it was the last thing running on the last TV working after the apocalypse, a large swath of the population really enjoy it who aren't an interesting advertising demographic and who may not have the tech and financial means to access it otherwise.

This is the system working: desirable content that couldn't be viably financed by the private sector.