As a younger listener to Radio 4 I find it very irritating that people constantly write in an complain about music in programmes, because I rather love it.
I have a technical suggestion for Radio 4.
With modern production techniques (keeping the voice and music mix seperate in a 5.1 system) it would be technically very easy to create a "voice only" version of Radio 4 FM on DAB, and the other digital platforms, and also for the legacy Long Wave service.
A mono signal, with only the voices would easily be carried in a low bandwidth channel (32k) - there will be some capacity spare when the Asian Network closes.
Such a service, which you could also broadcast for almost no cost on Freeview, satellite and cable, would provide more flexibility for programmes that do need to have musical content.
It would require that producers of programmes would need to have two separate mixes of each programme, but this is hardly a huge technical problem.