Also, what if the machine was broken? Or if there was an error in transcription? There are so many possible reasons why this message may never be decrypted.

Surely this would be tantamount to announcing to the enemy that you have broken their encryption scheme?

Yes. As such it would be a last resort and even then likely done very carefully (perhaps even to the point of burning a high level human intelligence source or sources as a plausible explanation for it). We're talking "no alternative" levels of desperation.

Why? You don’t need to be able to understand a cipher to produce plausible cipher text. You can take headers and footers from real messages and just drop in nonsense between. Or retransmit messages you recorded a few days earlier, or random mixtures of bits of real messages. The enemy still has to transcribe them, sort them out, reject the noise.

From what I recall of how Enigma worked, headers (and footers, if the concept applied) were also encrypted.

IIRC a transmission started with the rotor settings for the rest of the message encrypted using the daily setting and sent twice. Even sending this much, such that both copies communicated the same setting, would reveal that Enigma was compromised, I think.

You don't want to DoS the communication, you want for them to keep using it so you can intercept valuable information.

The coded messages were usually sent over the radio via straight key Morse code.

Once you have a few months experience in Morse code you are able recognize who is "talking" by the way they operate the key. The radiomen would know pretty quick if some new guy came started sending them bogus messages.