I don't think Lettman is saying these badges were not worn, what he is saying is that the Australian Army did not have the OSD badges that were common to the British and other Commonwealth forces. In fact the only authorised bz OSD badge I am aware of is the Aust Staff Corps badge introduced in 1935. Happy to stand corrected on that.
AIF officers no doubt had badges to their own specification of material or finish made up by suppliers in UK, the dies would have been in existence because Gaunt had already supplied Australia with the 'rising sun' pattern.
However the official badge authorised and supplied for both officers and ORs was the copper oxidised Commonwealth pattern badge, large for the hat. I'm not certain the attachments will attach but shown should be an extract from Orders for AIF 1915 for articles to be issued to officers, and AIF Order 1098 of 5 Feb 1918 which states Badge, Commonwealth, copper oxidised. Officers of the AIF were not authorised or issued a different pattern badge than ORs and that is the statement Lettman is making.
Eloquently said -- far more so than my rather subjective attempt. Thanks for the support on this one!