However governments rarely divest themselves of power once acquired, and so although many, many more folk are internationalist these years, there exists this relict of national control.
/stills rant about how in the United States, the Social Security was promised never to be used as a universal identifier.
Passports were referenced plenty in Around The World in 80 Days, written in 1873. ( http://aroundtheworld.phileas-fogg.net/80days.html )
Although if you mean the systematic use of passports, rather than their invention, yes - Wikipedia Says:
*During World War I, European governments introduced border passport requirements for security reasons (to keep out spies) and to control the emigration of citizens with useful skills, retaining potential manpower. These controls remained in place after the war, and became standard procedure, though not without controversy. British tourists of the 1920s complained, especially about attached photographs and physical descriptions, which they considered led to a "nasty dehumanisation"
While the modern-EU person can do this without any trouble, anyone from outside the EU (or the US), this is just a pipedream without serious legal money to throw at the visa manufacturing industry.
Nationalism is still heavily with us, and even more so than in earlier times.