I would have to disagree. My mother was a Western Australian and whenever I met up with family from over there I would be hammered with disparaging remarks about League or Union or Football because these were not the Australian game. Similarly with any contact with my Victorian cousins. My recent experience in Tasmania has been the same where you are ridiculed (considered un-Australian) in some circles because you are interested in any of the rectangular pitch codes. The feeling in the southern states and Western Australia seemed to be that Australian Rules was Australia's national game
I tend to think that the ones who dismiss Australian-Rules football are ignoring that it was heralded as the first thing AUSTRALIANS had created, not just British Colonials.
The reason being that football had been played in the colony from the early C19th. The football played was based on the game of Rugby as developed over the previous 200 years at the Rugby School in England. When the Melbourne Rules were written down in 1859 football had been established in the colony for over 50 years
The rules for the "Simplest Game" were drafted in 1862. This preluded the the "Laws of the Game", which organised what is now called Association Football. Technically, "Soccer" in Australia wasn't FIFA accredited until 1963.
The advantage Aussie-Rules has over Association Football (history-wise) is that it has no over-ruling body, such as FIFA. Therefore there is no logical claim to that statement.
No doubt the feelings have been exacerbated by the historical tensions between NSW and Victoria that arose when NSW lost its place as the "centre" of the colonies when Victoria temporarily became the wealth centre following the gold rushes in the 1850's and 60's.
That's new, linking a gold rush to differences in sport by region
Everything else you said makes sense.
I am not too long out of the Victorian State School system and I can honestly say that I never knew how Rugby (regardless of form) worked until I was 15. Moreover, we didn't get differences between League and Union.
There were regional competitions (for League I think), but few schools organised teams due to a lack of interest.
There were less than five Union workshops at High School in my time there, and none for League. My younger brother has a similar experience.
It is all about the Aussie-Rules, Football, Basketball and Cricket teams.
Personally, I fall asleep watching RL; and while I like the Wallabies, I struggle to understand Union.
"Soccer" is my number one choice, followed by AFL and Cricket.
I've played "soccer" competitively since I was 11, but also did Auskick for a number of years as a little boy.
I'm far from alone.