After the rise of German National Socialism, the American salute did not quickly fall out of style in that the American salute originated from 1892 and the National Socialist German Workers Party began in 1920 and grew through the 30's and beyond and Congress decided to try to change the gesture in 1942 AFTER the USA became involved in WWII. In reference to America's stiff-arm gesture, some Americans said "We did it first" and "its our salute" and everyone did not immediately embrace the hand-over-the-heart.
The stiff armed gesture developed because the Bellamy salute began with a military salute that was then extended out toward the flag. Also, Francis Bellamy (and his cousin Edward Bellamy) were not only socialists, they were nationalists, similar the 2 words added to the German Workers Party by Hitler. http://rexcurry.net/swastika3swastika.jpg
Using the outstretched salute is NOT a tradition that goes all the way back to the Romans, but that is a common myth.