Have border guards not always asked those questions? I'm pretty sure it's been like that since before the 20th century.
"[B]efore 1915 His Majesty's Government did not require a passport for departure, nor did any European state require one for admittance except the two notoriously backward and neurotic countries of Russia and the Ottoman Empire."
And it wasn't until 1945 that Americans were generally required to hold a passport to travel abroad during peacetime. [1]
An american in 1940 may not have needed a passport to leave, but would they have needed one to get in somewhere else? Surely the nations of europe at that time would have been suspicious of basically everyone?
People used to laugh at the Iron Curtain countries for asking such questions...
In the 60s you could board a plane without even passing any metal detector...