What would be worth charging money for is an app that could cache a configurable number of hours of new curated content when connected to wifi. Even so, that's not really any different from podcasts.
I feel like the world is still very much in a transitional state with regards to how we think about apps. NPR offers its stuff over the air for free, but you write some code to do the same thing with a computer, and suddenly people are saying it should cost money.
A lot of the available content categories aren't specific to New York, so it might be worth checking out regardless of where you live.
For example, if Planet Money produced a monthly bonus episode for, say, $5, I know I wouldn't think twice before tapping "Buy".
At least, that's how I would do it. NPR is missing out on a big donation opportunity by not taking advantage of an app store's built-in in-app purchase/donation infrastructure.
It was founded, initially, with funding from congress, as an independent, non-profit broadcaster. Currently, NPR receives very little to no funding from the Government. Something like 2% of NPR's funding comes from state, local, and national government. Though individual stations may receive radically varying amounts of government funding.
It is Public in the sense that it serves the public interest and is funded by listeners.
"According to the 2009 financial statement, about 50% of NPR revenues come from the fees it charges member stations for programming and distribution charges."[0]
NPR is not state media. That would be Voice of America, which is not allowed to broadcast in the US.
There is a good article here on its status:
http://www.npr.org/yourturn/ombudsman/2001/011228.html
"Legally speaking, NPR is a private, not-for-profit corporation chartered by the District of Columbia and qualified by the Internal Revenue Service as a "501(c)(3)" organization exempt from taxation. "
*edit - now seeing all the answers below