I'd wager the post-war proliferation was from soldiers who learned the song during WWII returning home, similar to Mademoiselle from Armentieres in the previous war. The song stuck around college fraternities and similar progenitors of bawdy songs (I saw it in a few college periodicals in the 1920s and 1930s, but none earlier than 1923), where they passed it down orally. Then, in war, soldiers, possibly from similar frats, or possibly just bored, sang them for each other, and then from there it took off.