When his country came calling, Frank Capra had already won three best directing Oscars in five years—”It Happened One Night” (1934), “Mr. Deeds Goes to Town” (1936), and “You Can’t Take It with You” (1938)—and had directed the incomparable “Lost Horizon” (1937) and “Mr. Smith Goes to Washington” (1939). He could certainly have rested on his laurels, but he was too patriotic an American not to assist in World War II.Too old to fight on the battlefield, Capra waged his war in the editor’s booth, constructing a series of seven propaganda films known collectively as the Why We Fight series,...