The reason, however (doubly so in Norway, which is basically as inconvenient as countries come for broadcasting purposes - lots of mountains and hardly any people) is that in DAB, you interleave a lot of channels in one data stream, transmitted from a single transmitter, whereas in FM, you need a dedicated transmitter for each channel.
The lower power bill is the major benefit seen from an operator's point of view.
Additionally, with FM you need to make sure no transmitters on the same frequency can cover the same area, as that would lead to interference. With DAB, they performed the brilliant trick of using multiple carriers to get the symbol rate on each channel very low; this means that if two DAB transmitters cover the same area, you get constructive interference - a signal boost instead.
The benefit of this in Norway cannot be overstated - we have (literally!) thousands of low-power FM relays to cover every nook and cranny with broadcast radio. (Denmark, home to a larger population, had a handful of FM transmitter sites.)
Hence network planning is a lot easier in a DAB network.