They weren't.

What you seem to believe has more to do with the process of nation building and general ethnogenesis that happened progressively in *WASP Commonwealth countries after WW1 and up to this day. WASP British people in Australia, WASP British people in Canada, WASP British people in New-Zealand etc. started to stop considering themselves as being British and started adopting new identities : Australians in Autralia, Canadians in Canada, New Zealanders in New Zealand etc.

In this construction of a new identity, new things were found to be proud of, as a people, as a nation. And WW1 is probably one of the most important for all theses nations.

And I can assure you that Canadians, Australians, New-Zealanders will all pretend that they were a cut above others Commonwealth forces, or that the particular battle their "countries" (wasn't that at the time) fought in was one of utmost importance and changed the course of the war.

In reality the troops from thoses countries represented a really small part of the overall Commonwealth forces mobilised by the British Empire, and weren't seen as being particularly formidable by anyone.

Also, many, if not most, people living in Canada, Australia and New-Zealand were from recent migrations waves from Britain, and had actual memories of Britain, or had people in their families (parents, grand-parents) who had theses memories and most saw themselves as British. So painting thoses troops as "Australians", "Canadians" etc. is actually quite misleading because the meaning of these words has considerably shifted since WW1, and now imply a certain identity that purely and simply didn't exist at the time. It's not to say that thoses words weren't employed, but they didn't have this meaning of a distinct, separate national identity from Britain. For instance, in Canada, the term "Canadian" was still often only refering to the French speaking population of Canada well into the 20th century.

For the same reason, speaking today of the War of 1812 as a war involving Canada makes absolutely no sense, unless the people you're speaking to are aware you're not refering to today's meaning of Canada, implying a certain national identity, but to the part of the British Empire corresponding to the lands north of the USA circa 1812

*I precise WASP because the Commonwealth was, and still is, composed of Nations and cultures that existed before Britain colonised them, and weren't an extension of the cultural and national identity of Britain, and so never really had to wonder what they were in relations to Britain once independant