The BBC doesn't produce all the content they show.
Rights owners have considerable control over what happens to the content.
Thus, many BBC radio programmes are downloadable as MP3 and can be kept forever. An excellent programme In Our Time[1] has made their entire back catalogue available, but a programme that has music (Desert Island Discs, or any live concerts on BBC Radio 1) will have much more restricted download conditions.
iPlayer (hateful stupid ridiculous name) really is amazing. The BBC led OnDemand viewing in the UK. And what we've got now is very very much better than the RealAudio kludge we had years ago.
So, really, the target here should be stupid rights holders who don't understand the benefits to greater viewership.
They need to come up with some other way of paying people who create content. The BBC is (at least, I hope they are) collecting a lot of data about how often programmes get watched or downloaded over their various online services; so maybe payment could be linked to download amounts somehow.
Paying content creators in a better way would also help "archive" services like BBC Radio FourExtra, which suffers from heavy rolling repeats.