Radio brings the current news at the top of every hour. You know that the news doesn't just happen once an hour, don't you?
Radio-on-demand news should be like Web news: a compilation of the latest news stories. You could offer compilations of different length (5-minute, 10-minute, 30-minute). Modern radio stations have all the clips and manuscripts in digital databases so all you need is to make it available to the public. It's no headache to make, but no one does yet, as far as I know.