I wonder why they keep using a dedicated numbers station instead of embedding the code in a regular radio broadcast on a traditional channel? I'm sure that even before LLMs one could find a way to create a story where certain numbers / code words would be embedded without altering the underlying story too much. And they could probably get BBC / whatever station to air it. It would be a bit less inconspicuous to listen to BBC than to a dedicated numbers station, even if the message would be undecryptable either way.
I can't find it immediately, but I've read about something even sneakier than this. A standard broadcast station was modified such that its carrier signal was modulated by a PSK signal. The intended listener would use e.g., a PSK-31 modem to listen to the carrier signal and would be able to obtain the encoded digital data. Everyday listeners would hear the regular broadcast. The station involved _might_ have been a BBC station, but I don't recall.
who's to say they aren't doing both? They may not even be sending anything over the number station; these stations will continue on a schedule even when there is nothing to say and nobody is listening because it makes it harder to eek out a foothold in the event of a weakness in the encryption.
Seems to me like coordinating with an entity outside of the spooks' control, such as the BBC, would give more opportunities for leaks. It would also reveal some information about who is controlling the signal--someone with some kind of relationship with the broadcaster.
regular AM/FM stations are not broadcasting on shortwave bands
Shortwave propagates better and also its just a one time pad being distributed so embedding doesn't matter as much as long as the one time pad is longer than the intended message to send. There is no way to decrypt it because once you encrypt a message using a one time pad it is impossible to decrypt without the exact one time pad that it was encrypted with.