The US, Australian government are giving support to Abe administration because it is in their best interest using another Asian country to contain China rise.
It's the favorite pastime of Chinese leaders, pundits, and laobaixing (老百姓) to cry Yankee containment, but that's simply wrong. The US isn't trying to contain China because;
1) If the US really wanted to contain China, it would look a lot like how America treated the ex-Soviet Union
2) Sino-American trade is at around $500 billion, and US moves to contain China would damage the American economy too
3) US needs China to keep buying Treasury Bonds. Containment policies might dampen her enthusiasm for US debt
4) Nations around the world would oppose/resist US efforts to contain China, including many American allies
5) Hostile moves against China would drive her closer to Russia
6) Is it even possible to contain the world's second largest economy? I think that ship sailed long ago.
7) Even if it's possible to contain China, the US wouldn't do it because she understands a weak and poor China could cause more trouble than a strong and prosperous China
Japan seek leadership role in Asia.
So??? If projections are correct (yes, big if), then China's economy will be about 3-4 times bigger than Japans by about 2040. Japan may lead the anti-China alliance with Philippines, Vietnam, and Australia, but so what? It wouldn't make much difference if China continues to enjoy peaceful development for another 30 years.
Partnership with current Japan administration is not possible with Abe being in charge and that's a good thing. Here, we could see the anti China forces under one nest and easier for China to find out who's their political nemesis in Japan. The current situation will continue as it is, and only China can do now is undermine Abe administration using whatever means necessary under their disposal. Probably the CCP have to wait a few more years. Democracy will change the Japan administration to a new one. Just have to wait it out.
The quickest way for China to wreck Abe's administration is to leave it alone. The Japanese people will sink Abe soon enough.