In Germany, public TV is paid for by (nearly?) every household. [0]
Forcing everyone, including poor people, to subsidize rich people's taste for documentaries seems a bit.. off?
Similar arguments apply to public libraries and opera houses, though at least there the financing is done mostly via progressive taxation.
Of course, you can argue that we sophisticated people know what's good for those unwashed masses, and if only they watched their documentaries like they are supposed to, they would soon see the light. Colour me skeptical.
[0] As far as I am concerned, private broadcasters can and should do what they feel like.