Are you seriously suggesting that commercially written songs from the WWII and post-war period are outnumbered 2:1 by traditionally generated material ? I can't believe you are but that's how I read your post. I really think that I could find many commercial songs from the period that are still well known and performed for any one definabley "traditional" song. (Using the definition of traditional I gave previously).
My point wasn't that "traditional" songs didn't exist. simply that the vast majority of songs that survived the era were commercially produced because they constitute the vast majority of available songs in the era, and that's because the culture from which "traditional" songs could arise was lost to us by the middle of the 20th century.
My main point, which I stand by, is that traditional music, in style and form, has fallen into the hands of a minority as the entertainment industry has expanded and that this process has been going on for about 150 years.
POI: Lili Marlene did come to the allied troops via Armed Forces radio, But it was the German Armed Forces radio ;)