If this catches on, it might disintermediate (EDIT: or accelerate the existing disintermediation of) the local public radio stations, which will then lose donations, which will then be less able to do local reporting. (Of course I'm not sure our Houston public radio station does all that much local reporting to start with.)
Just glancing at the app, I don't think there is anything here that you couldn't currently do in the NPR app ecosystem. For example there is already an NPR app that lets you choose radio stations or just programs from around the world and a lot of local stations built their own, independent app (though in my experience those are lower quality)