Six Music has the BBC music and sound Archive at it's disposal, anyone 'taking it over' just wouldn't have that wealth of archive sessions nor would it be able to keep the presenters currently working at the channel or attract the performances that it currently does. Nor, as Chutes just said, would another broadcaster allow presenters to play the variety of wonderful music that six music currently does.
Most of the current presenters won't be left without work, many of them aleady still do programmes for Radio 2.