I think the standard answer would be that a second Constitution emerged from the political process. This “Second Constitution”, not found in any one Act but created by a series of conventions, kinda sort emerged from the first-the actual Constitution. This seems like BS to me but that’s what they say.
The first Prime Minister, Edmund Barton, had a Ministry and Cabinet like any other PM and as far as I can glean from Wikipedia, was for all intents and purposes the chief of the Executive Government right from Federation in 1901. The Federal Executive Council has never been of any importance and may never have existed at any stage in Australia’s history.
Practically speaking, it may be difficult for the body that makes new legislation, ie the Parliament headed by a Prime Minister, not to also be the executive as well. As both the drafters of the laws and representatives of the people, they are more familiar with the practicalities of new laws than the Governor General and the Federal Executive Council. At least that’s what those arguing for the historic arrangement might say.
The way the Governor General is appointed “at the Queen’s pleasure” is something that confuses me as well. Perhaps the system we’ve had historically is more democratic than if we’d followed the letter of the Constitution. The same question arises, though. Why has this been dead in the water right from the very beginning?
I’ve known about the discrepancy between what the Constitution says and the “Second Constitution” for many years but never gave it much thought. I never thought it was particularly sinister but maybe it is when you think about it. If something like who is the head of the Executive can be so completely at odds with what is written down, then what’s to stop them from disregarding anything else in the Constitution they wish to disregard? States refusing entry to non-residents, mandatory contact tracing, vaccines, quarantine for the healthy and face masks, banning international travel, rule by decree. what else?