I think this has happened in part already. Although I try to listen to my local station (KUT) via their app, I also use the NPR app to time shift programs like All Things Considered that I tend to otherwise miss. (If you miss a program by an hour or so, the NPR app won't let you listen to a program that's within some window of its broadcast time, but you can listen to it any public radio station currently broadcasting it.)

I also listen to shows that aren't carried locally, and of course, time listening through the NPR app is time not spent listening to KUT directly (which I probably would do if there weren't alternatives, because I'm pretty much an NPR junkie).