In January 1942, as the United States committed itself fully to World War II, President Franklin Roosevelt decided that baseball, then the national pastime, should sustain civilian morale during the lengthy struggle ahead. He implored its commissioner, Kenesaw Mountain Landis, to make sure the games went on, despite worldwide armed conflict. And so they did. Professional baseball players, Roosevelt argued, “are a definite recreational asset.”

Roosevelt did not extend that consideration to professional football players, whose sport did not register …