I see that the BBC is to introduce new DAB only channels as "spin offs" of their main radio channels, including a Radio 2 lite that will play popular music from the 50s, 60s and 70s, competing with the likes of Smooth. Radio 3 will also get an easy classics outlet that will go up against Classic FM. There will also be two Radio 1 based channels.
Apart from the possibility that the commercial stations will resent the BBC jumping into "their" pond, they may see it as unfair ad-free competition.
Where the BBC may come adrift is that they won't understand that their main stumbling block is that they don't have an easy streaming option, but force potential users to use the BBC Sounds portal, which is inflexible and requires users to log in before listening, which may be fine for the committed, but is a barrier to potential and casual listeners. Listeners to Smooth and Classic FM don't have to jump those hurdles to stream their music.