It's one thing to put out statements on Australia's concerns about ADIZ vis-a-vis Pacific region stability, but quite another to dive headfirst and insert itself in an essentially bilateral argument between China and Japan.
Australia...inserted itself into a Great Powers game deeper than it needed to do (to show support for Japan), and unnecessarily harmed the carefully crafted Sino-Australia strategic partnership PM Guillard forged. It's going to be a bumpy ride ahead for China-Australia relations.
Any nation can raise its objections. South Korea, the US, Japan, Taiwan, and Australia have all raised their objections.
All of them also have to live with whatever fallout results from it. There is no doubt that they all (including Australia) took this calculus into consideration when making the objections and determined that what they imagined the cost would be was somehow worth it. In some cases it was purely to serve as a marker for, as you say, nations with treaties with one another.
With others, it is either economic or political. For example, Australia is seeking Japan's significant technological help in building its own new modern and stealthy diesel-electric submarines to replace the Collins Class. I have no doubt that things like that factored into it.
In the end, it is my contention, that none of that will impact the ADIZ.
China has established it. I believe it's principle purpose is to protect the Chinese mainland and any sensitive installations on the mainland from any aggressive or threatening flight profile out over that portion of international air space in the Pacific.
The US, Japan, South Korea, Taiwan, Australia, and many other nations have similar zones for the same reasons.
I do not believe that any of the objections were made in the real hope that China would do away with the new ADIZ. As I have stated, I believe that ADIZ is here to stay. I also believe the PRC will use it for the stated purposes and that when used in that manner there is no realistic way that these other nations can object to it.
So what you are left with is political markers being laid down for what each nation believes are in its own interests that serve to try and strengthen either existing ties, or desired ones...and may be at the cost of others that are developing.
But in the end...they will not have any real impact on the ADIZ itself.