I think the BBC might struggle with that idea. Everything the BBC puts out on-air on any of its radio stations, whether a documentary, music show, news or anything else, is automatically made available for on-demand listening via
BBC Sounds, which is also where you go if you want to stream any of its radio stations. The stations don't even have
websites any more, just pages on BBC Sounds. The live streams can be played with, too - you want to hear a song again, or missed a bit of an interview? Just go back a few minutes and hear it again.
If you listen to any BBC radio nowadays, there is very little mention of FM frequencies or live broadcasts, it's very much "on BBC Sounds" all the time. For instance,
this recent TV promo for the Gen-Z-targeted BBC Radio 1, which doesn't mention the national FM transmitter network at 97-99 MHz, or even DAB radio, but is just "listen on Sounds".
You can see from the tone and type of content on Sounds (mindfulness playlists, Pride mixes etc) that they are targeting a younger audience who may well no longer even own a radio.