That idea has come up from time to time, and while the expense is minimal for broadcasters, it requires consumers to buy new radios. That's the same issue for HD. We can see how well it's worked for HD. The general view is people don't buy single-use radio devices any more. Combine a radio with something else (like a car or a phone) and you'll sell a few. That's also the case for satellite and internet radios. Radio-only devices are non-starters, and the electronics industry has no motivation to sell them any more.
A good example of what you are saying involves XM's early efforts to sell stand-alone home or workplace satellite radios. They worked OK in the vicinity of the terrestrial repeaters, but generally in most indoor locations were as useful as a brick with knobs on it. Nobody bought the single use radios.