Taxes are not free to manage and collect so this also provides cost savings.
We have this debate periodically in the UK. The argument against abolishing the TV licence is usually that a dedicated tax ensures a larger independence of the BBC, which is not "at the mercy" of the government for funding, but I think this is a rather weak argument because the government already ultimately decides the amount of the TV licence fee, which is a tax.
Edit following the "reactions": By the way, in the UK it is not allowed to criticise anything related to the BBC (and the NHS) as you can see. Is it the same in Germany? :(