My suggestion to Later would be to add a series of specials to the schedule. I seem to recall that in the early days Jools went to New Orleans for a show about the music down there.
There have been, and still are, plenty of gigs that Later could cover. a few years ago Jeff Beck at Ronnies, this month Jon Cleary at Ronnies. A couple of years ago Keb Mo at the Union Chappel and Vulfpeck and Vintage Trouble. . . all missed. The Funk Brothers came to the Festival Hall in 2000. In 2005 the Muscle Shoals, Hi and Stax studio guys came over and played at the Barbican. All these gigs should have been covered, but they weren't! There must be many examples in other genres.
Never mind knocking what is already on TV, what about all the missed opportunities?