I suppose it's no surprise that Mark Thompson doesn't understand the whole basis of UK popular music culture, and thus wants to axe 6Music.
No one these days calls for the closure of Radio 3, as they did in the past, because the remit is so very clear.
Since the late 1970s there has been a clear subcultural divide between those who regard the 'performance' as the artform, and those who prefer the 'recording' as the focus.
On the 'recording' side falls Disco, Electronica and Dance, as well as the US cultural import of Hip-Hop and Jamacian influences from Reggae to Dancehall.
Much of this comes with the rise of the video, as this often forms part of the final 'product'.
The producer is king here, and mixing and remixing part of the mix.
Into the 'recording' side also falls most of modern 'pop', in the Simon Fuller mould.
On the 'performance' side is Punk, New Wave, all forms of Rock, Metal, Death Metal, and both UK and US forms of indie music.
Those in the 'performance' camp will see a live performance as a vital part of the music. The band or artist must be able to perform live, and a recording is just a recording.
Here the writer, composer and performance is held in the highest regard.
So, whilst Radio 1 covers the 'commercial consumerist pop' bracket (the stations supports the bulk end of the music market), and Radio 2 tends to cover pre-1977 music-era genres for those too old to care about it.
This has left Radio 1Xtra with the 'recording is art' modern genres, 6 Music has provided a cultural environment for those in the 'modern performance' camp.
Yes, there is a huge amount of crossover, as you would expect within the musical hyperculture we have in the UK, but the BBC needs to provide a full-time service for those who have a cultural need for new performances and classic recordings.
In an world with Spotify and iTunes (not to mention torrents and other peer to peer), 6Music could probably never play a single old track that wasn't from the BBC archive and only play new music.
So, I would suggest to Auntie's Digital Doctor Beeching that 6Music be supported because it forms an important support the the UK's musical culture.