That's the reason for the Rundfunkgebühr instead of taxes. Keep it a bit further away from the state to limit its influence.
I know we want to avoid ending up with super-polarized media like the US, but I don't believe this is the way. I don't know what the way is, since you also don't want to give airtime to the crazies, and I feel the market for sane conservative news shrinks by the minute.