It has always perplexed me how WWII US cryptographers managed to get anything done, when the plaintext still looks like gibberish -- further complicated by a novel encoding betweeen a non-western script and EM signals.

I believe the Germans had a policy of starting every message with some standard boilerplate, so Allied cryptographers were usually able to perform known-plaintext attacks with only passive monitoring as long as they observed any one message while it was still unencrypted.