I'm assuming the OP is in the UK or Europe. In the US the only OTA digital radio service we have is HD Radio, which is about as popular as week old fish (there's also satellite radio - XM Radio - but that's a paid service). And it was designed as an add-on to analog FM radio, so if FM dies, so does HD. I have seen that most new users on AK specifically mention that they don't listen to FM, but we do have a veteran users that do. I personally don't listen to it any more for music (occasionally NPR) because most radio stations in NYC have been taken over by massive corporations and they play the same things over and over.
I don't know the details of DAB, but I do know it's actual radio, which means it has a tuner that receives signals via an antenna. These days, almost everything in mass market audio is done with ASICs (application specific integrated circuits), all controlled by software/firmware, so at most it probably means the addition of a chip or two, plus circuit board traces to wire it all in. Costs them very little, and this way they don't need to customize the circuitry for different markets where analog radio may be more popular (although you won't see DAB-capable receivers in North America).