No. He really isn't.
His country is, though, certainly, and he has spoken as his government has asked him to, which is his duty as a constitutional monarch.
And, you're right, Australian governments tend to be committed to this stuff as well. It might not make sense for a superpower like America to sign on to things like this, but smaller, less powerful nations tend to see it differently.
It used to be a bit different when we thought we could rely on the United States to support the nations that supported it - but that ship sailed a long time ago. Nobody has any reason to trust the US anymore. Not since you started electing people like Clinton, and Obama, and Biden.
Good Sunday morning chuckle: Local news reporter today innocently described Camilla as “Queen Corset.”