Be nice if they'd show some contemporary jazz. The country is swimming in it.
The Beeb, however, has jazz (folk, classical too) as part of the heritage industry. All you get, if you get anything, is the 'Jazz Giants' of the past. There's a place for that, but it would be nice to have a TV version of Jazz on 3.
Pipedream, of course. Wouldn't get past the first suggestion.