Australia was settled by the British. We still have the Queen as our head of state, and so are still a part of the ommonwealth.
The US wanted political autonomy from Britain, but was only able to get it through a revolt against the British.The Commonwealth exists because after the US obtained its independence, Britain wanted to retain some vestige of Empire and to maintain the economic and cultural ties with its former colonies. In other words, if independence was inevitable, there's no reason more people had to die like when George III was running the show.And not all the commonwealth countries have the Queen as the honorary head of states...........
US told England to kiss off in 1776
even though we are part of the commonwealth England has no control over Australia.