Conversion of television and conversion of radio are two completely different things. With television, the first difference is that a majority of television viewers get their signal indirectly through cable/satellite/etc and the conversion meant nothing to them. Second, even for those who use the direct over the air signal there was an easy way to add an additional box to convert the new signal to an old style one. That's not nearly as easy or even feasible for FM (or AM for that matter where it's needed much more.) Also, the boxes that TV's added to convert to digital were paid for by the auction of part of the TV spectrum. That's not going to happen with radio. Think about all the places where people use AM/FM radio. Cars, portable radios, even cell phones that have FM receivers are not going to be able to be easily retrofitted. If we were in 1940 and the only radio we had was a big piece of furniture in the living room then we could do this kind of conversion without much of a problem. Listening today on that kind of device is a tiny minority of total radio listening. That's why all of the IBOC digital that in use today is a hybrid analog/digital. Anyone trying to go all digital is committing suicide.
At work, I just listen to audio streams on my work computer, wearing headphones. At home, I listen to audio streams on my iPad and a Bluetooth external speaker. In other words, I use a traditional radio only when I am in the car. Cars are a niche for traditional broadcast radio that will erode over time, as more and more cars are equipped with iPhone docks.
I would argue that widespread mobile streaming is unsustainable. Mobile networks are being stretched right now, and there's very little mobile media streaming. Every single person streaming needs their own bandwidth and that just can't scale. What I do think would work is something I haven't heard of anyone doing yet, which is to create an app (a Spotify/Pandora/whatever clone) with a custom playlist that would be downloaded ahead of time (probably at home through WiFi or USB) and then played back on demand when you're in the car or wherever. The problem with that is the record companies might complain if there isn't DRM and that introduces all sorts of issues.
Broadcasting is the most efficient way to distribute media, but it has drawbacks. I don't think it's going anywhere anytime soon. People have been predicting the demise of radio for 60 years and it's still here.