In The King's Speech, the scene where the King gives his first Wartime speech, is accompanied by Beethoven's 7th in a Crowning Music of Awesome... that is until the viewer realizes that Beethoven was held as a paradigm of German culture by Hitler, and was most certainly used to represent the German war machine. Then the viewer realizes that this only serves to mark the further awesomeness of the speech. The music represents the impending German attack. The speech was not only for the British people, but an announcement of defiance to Germany. The King was speaking in defiance, and is heard over, Beethoven!
There is a certain irony here, in the Nazi veneration of Beethoven. His Symphony #3 Eroica was originally dedicated to Napoleon. When Napoleon declared himself Emperor of France and touched off a decade of warfare, Beethoven tore up the dedication page, declaring "Now, too, he will tread under foot all the rights of man, indulge only his ambition; now he will think himself superior to all men, become a tyrant!" It's pretty obvious what he would have thought of Hitler and Nazism.
It's also worth remembering that Beethoven wasn't just Music to Invade Poland to. The Allies used the opening bars of Beethoven's 5th Symphony as shorthand for "V for Victory": The Morse Code for "V" is the opening rhythm of the symphony, "dot dot dot dash".
When George first meets the speech therapist, it's established that he can speak written text perfectly fine without any training if he's listening to music and can't hear himself. While this trick wouldn't work for public speeches, it would have worked for the radio address. Instead of relying on a whole host of other tricks, which clearly put him under a lot of strain and force him to use odd pronunciations like "uh-people," George could have simply tuned his headphones to some loud music.
The point of the therapy was to allow George VI to be able to speak anywhere. So it would be best to use techniques he could use anywhere.
Also, have you ever tried to deliver a speech while there's music in your ears so loud you can't hear yourself? It's very difficult to know whether you're projecting loud enough for the apparatus, whether you're emoting enough for the language you're using, and whether you're going too fast or slow. Oration when you can't hear yourself is 'hard'.
Yeah, he can't use the music-listening technique everywhere, but why doesn't he use it anywhere? It would be quite easy to listen to music while speaking on the radio.
This Troper thinks that George did not want to have to rely always on the music as if it were a crutch, and he knew that he would be required to make public speeches, so it makes sense that he doesn't use it on the radio.
Him making that choice is nowhere in the film, and it would radically change the complexion of the climax if it were. It also wouldn't make sense given that the way he does deliver the speech is also unacceptable for public addresses. Logue stands in front of him and whispers directions to him throughout the speech. If George didn't want to use a crutch, he would have asked Logue to step away and let him do it himself.
This Troper has read The King's Speech, a book that further elaborates on the movie, written by Logue's grandson and based on Logue and George VI's private papers. There was always the option to record, and infact each speech was pre-recorded with music etc. as a backup. However the BBC Director-General, and the King himself, were both of the opinion that a live speech created a better effect. Also, while Logue did assist in the speeches, his primary role was to change difficult words to easier words, help Bertie rehearse, and in real life when the climax speech happened, Logue actually told the King he wasn't needed anymore, to which the King disagreed. Also, for that speech, Logue's role is that of conductor; they're pulling out all the stops to make sure that this one speech suceeds.