It once was a big day in the United States, an end-of-autumn Saturday when, inside the walls of homes in huge cities, small towns and rural hamlets, everything seemed to stop for a few hours.

The black-and-white television sets would be turned on, the shades in the rooms drawn or lights dimmed to prevent glare. The families would gather—this was the fathers’ afternoon, and their children, almost by osmosis, knew it—and something quietly momentous would unfold on the screen: the Army-Navy game. It was considerably more than...