Actually, much radio was recorded, for rebroadcast in market that couldn't be reached live. They were recorded on huge vinyl discs called "transcription discs". They were 16 inches (just under a half metre) across, and many still exist. (Bob Hope kept the copyright on his and all the discs of his shows. I have some commercial CDs of his shows in WAV format, made from them, the sound is mono (of course) but top notch, as good as it would have sounded when broadcast.
However, most radio shows didn't bother, and the public didn't have access to the equipment to play them back, so they often got junked. Even today, there isn't enough market to justfiy high quality transfers from the existing masters. (Bob Hope released around 20-40 shows during his lifetime, they didn't sell enough to keep re-releasing them. He did a show a week for 20 years or so, that's around 1,000 shows.)
TV is more of a mixed bag, sometimes it was recorded with a specially synced movie camera (synced at 60 frames a second) filming a matching TV screen, sometimes not. This technique was call a Kinetoscope. Once again, there is no market for old Kines, a hugh hoard of early '50 to late '50 Kines was found in an abandoned mine in the Sierra mountains, under perfect storage conditions, but nothing has come of it, no market exist to make it worthwhile to transfer...
For more detail on "transcription discs" here's teh Wiki link -
http://en.wikipedia.org/wiki/Transcription_disc