Also, while number stations broadcast over the air, the signal might not terminate at a radio receiver. It might be picked up by another system and forwarded in a different form.
A similar model is used by Chinese FireDrake jammer. There are numerous broadcast stations for FireDrake and all are fed by the same satellite radio channel (one of the audio channels of the minority radio stations) which play extremely high intensity chinese classical music which loops perfectly and lasts 60:00 minutes sharp.
When they spot a transmission they don't like, they tune the ground station to it and blast with the music. Intensity of the music drowns out the other transmission. Interesting stuff.
Also, low tech stuff is extremely resilient to outside effects. Modern IP telephony will collapse if something bad occurs. POTS, won't sneeze at it probably.
It's almost more suspicious to be listening to a radio at all these days, so unless you needed coverage of areas without internet access it would make sense to just dump the numbers onto a .onion or similar.