My portable radio of choice ...
It's hard to beat a landfill android or an ancient iPhone in a decent speaker dock.
Use your home WiFi in and around the house, or use 3G elsewhere; in fact my 3G service is better than my landline internet even in the house.
I should think one could make something quite nice with a Pi, a touch screen and a USB freeview dongle. DAB, on the other hand, seems to be a solution in search of a problem.