I cannot answer exactly as to 'why' the BBC have this trdition, though knowing the BBC I would hazzard a guess it is related to their 'superior' attitude and their liking to be better than their tv/radio rivas.
However, I am very GLAD they have done things this way.
Just using Queen as an example, the album Queen at the Beeb is a fantastic album, and the different versions on there are terrific.
I am one who likes to collect as many 'studio' versions of songs by Queen as possible, and so QatB is an invaluable part of my collection. Having the rest of the songs they did in those sessions (not included on the album) also makes my collection much more interesting and varied.
Take 'Son and Daughter' for example - a fantastic version employing the solo that was part of the progression that led to Brighton Rock (started with Blag by Smile of course, I believe). Brian played that solo Live very often back then before Brighton Rock was recorded, and it is very much inspired by Jimi Hendrix. The fact that there are little or no 'official' versions of Son and Daughter released with that solo in it means that QatB is an invaluable source for tracking the rise of Queen and the development of their songs.
I am sure the same can be said of many other bands who have used the Beeb as their playground in their careers.
If you're searching out for something,
Don't try do hard.