That's a bit like asking healthy people. You'll get answers ranging from things like exercise to homeopathy.
Answers from people can be used to suggest avenues for investigation, but shouldn't make you fund expensive stuff outright. (Assuming here that homeopathy is obvious nonsense, that people still swear by.)
And, of course, public libraries and documentaries don't have to just produce good effects. In order to justify public funding, you'd need to do a whole cost-benefit analysis and look at opportunity costs.
So look at what you get from public libraries vs libraries financed from private charity _plus_ whatever other good things the public money saved could do (including just outright giving it to poor people).
I deliberately picked public libraries here as a provocative examples. I suspect they might actually pass the cost-benefit test without too much contortion of metrics and data.
I am much less sanguine about the bang-for-buck of publicly financed opera houses, theatres and symphony orchestras, which Germany is quite fond of. And of course, publicly financed radio and TV broadcasters.