Yes it’s quite true that in 1920, the League of Nations organised the Conference on Passports, Customs Formalities and Through Tickets and a common format for passports was adopted. All very sensible. As I said in an answer to another question on this topic, it makes sense to have them the same size and shape and to be machine readable.
The big difference between the League of Nations’ proposals for a common passport design and the current passports issued by EU member nations is that the older passports did not purport to be “League of Nations” passports and did not have the name of that organisation emblazoned on their covers preceding that of the issuing nation. There is no doubt that the Euromaniacs like the idea of the documents being thought of as “EU” passports. There is no such thing because the EU cannot (yet) issue passports in its own right. So to support its ambition or even pretence to be seen as a sovereign state it hijacks the passports of its members. It works too, because time after time (and even within at least one answer to this question) one sees references to “EU Passports”. At least when our passports are redesigned the UK will no longer be party to that ridiculous pretence.