Lots of artists have released albums of BBC Sessions since that Beatles release - The Who, Led Zeppelin, The Kinks and David Bowie to name but four.
The Beatles release is really the tip of the iceberg. I remember taping a 'Beatles at the Beeb' radio series in the late 80s and it was something like 10 programmes. There's an even more complete anthology available on bootlegs.
See here -
http://musictravellerstwo.blogspot.co.uk/2011/11/beatles-complete-bbc-tapes-purp...As with a lot of TV performances from the 60s, the problem we have is that a lot of recordings were wiped in the early/mid 70s for storage purposes and are no longer in the archive. Clearly someone in charge with a few brain cells missing didnt see the historical importance of them so there are several performances on TV and radio by bands like the Beatles, Stones and others - and even a Bob Dylan BBC-TV concert special from May 1965 now exists as an audio recording only.
There was a 'Stones at the Beeb' radio broadcast in November 1985 which gave us several performances which were previously uncirculated so there's some hope that there must be more. My opinion is that had there been
significantly more, they'd have maybe had another broadcast at some point in the last 28 years (I'm talking about in-studio radio sessions for shows as opposed to broadcasts of concerts such as Leeds 1971) and its worth remembering that the Stones never did any BBC radio sessions after 1965.
There was talk in early 1998 of the possibility of a Stones BBC sessions album with about 40 'unreleased' songs (whether that means 'unbootlegged' is doubtful) but nothing ever seems to have came of it. I dont imagine that the band's relations with ABKCO are a factor - there's been a lot of collaboration in recent years (things are easier than they were in 1998) and I was surprised they didnt do something in this vein for the band's 50th anniversary.
I think it'll be released sooner or later. Hopefully they wont leave it SO long that there'll be no one around to care by the time they do.
Meanwhile, this is what exists that I know of :
http://rocksoff.org/radio.htm(might need a bit of updating and revising since I compiled it, but not much)