The ANZAC's were very important to the war effort, without them any attack into the Dutch East Indies would have had to either be launched and supported from India, or all the way from the US West Coast. With minor stopping points like Samoa, and Fiji. While bases in places like New Caledonia were critical for the drive up the Solomons they lacked the space and infrastructure to underwrite the effort.

Australia served as that great supply depot and port for the initial counterattacks against Japan in the Solomons, and up through New Georgia, New Britain, New Guinea, and on. It allowed units and ships to rest and refit without having to be shipped back home on a months long journey, and eased the logistical burden on places like Pearl Harbor and Colombo. Instead convoys could depart from California or elsewhere and go directly to Melbourne or Sydney.

Darwin and other ports also served as key bases for the USN submarine effort which slowly strangled Japan of its precious lifeblood and resources for the empire.

In practical terms too we can look at the efforts made by the Allies to protect Australia to asses its value.

The Battle of the Coral Sea represented an investment of 2 of the 4 carriers Nimitz had on hand to defeat the Japanese invasion of Port Moresby, with a 3rd task force on its way. Nimitz and King were very concerned with keeping Australia and the sea lanes to the US open.