One-time pad encryption is unbreakable in principle, and intelligence services documented its use with shortwave broadcasts aimed at agents abroad: the Conet Project published four CDs of recordings in 1997, Cuba's Atención station was cited in US espionage trials including the 2001 Ana Montes case, and Poland prosecuted a spy in 2014 partly on numbers-station evidence. Several stations were traced to government transmitter sites.
The famous stations earned nicknames from their interval signals, the Lincolnshire Poacher, Swedish Rhapsody, the Buzzer. Listeners built entire catalogs from their bedrooms and every official request for comment was met with silence or refusal, which made the hobby feel like trespassing on something real.
The durable logic: shortwave needs no infrastructure at the receiving end, leaves no log, and reaches anyone with a cheap radio. As long as states want deniable one-way channels to people they will never acknowledge, the cheapest technology in the building stays on air.
If no government admits these exist, who pays the electricity bill?