I can't see it happening, the incentive just isn't there.
For home use, we now have internet streaming radio, which offers a wide selection of stations and no inherent limit on bit rate. A better DAB doesn't offer anything new.
For car use, streaming internet may well happen anyway; it'll depend on the roll-out of 4G and whether or not the networks can manage an infrastructure that actually delivers the rates of which the technology is capable, rather than just being able to tick a box that says "yes, this area is covered by a 4G signal" despite the backhaul relying on Morse operators and carrier pigeons.
The BBC already has perfectly good coverage on FM, so the real (ie. commercial) benefit of a better DAB would be the ability to stream more adverts into cars. Since the ads are the very reason I rarely listen to commercial radio anyway, I can't see the market being there to support a new technology roll-out.