I think the radio is ahead of the TV if you have cable or Satellite. If the radio broadcast is on the Internet, you might be able to pause it like a DVR to sync it up.
Several years ago I thought about designing a device that would basically be a radio with a delay function but I figured it would be too much of a niche market. Maybe Jerry would fund it...
I would definitely do it if DVRs had an audio input because most people want to pause the game occassionally which you couldn't do if listening to the radio.
I could design a DVR type device with an optional audio input but it would have to connect to the Satellite or Cable box because the Satellite companies won't support 3rd party tuners as far as I know. Tivo's didn't have audio inputs.