Why is the King represented by a Governor-General?
The Australian Constitution is established under the Crown which means that whoever is monarch in Great Britain is the monarch of Australia. However, the monarch is always represented in Australia by an Australian as Governor-General and, once appointed, the Governor-General assumes the role of executive head of state and oversees the Australian Constitution. The King plays no further constitutional role in the country other than retaining the residual power of dismissing the Governor-General.
That power is always exercised on the advice of the Prime Minister and the benefit in this indirect approach is that because the Prime Minister cannot by himself appoint or sack the Governor-General, the process becomes transparent and open to question by the public and the media and is therefore a safety valve and an important part of the checks and balances which pervade our entire constitutional system of governance.
Whilst the Governor-General may prepare a report for the King on what is happening in Australia, that is only for information purposes. The King never interferes in the governance of the nation.
People may ask “why doesn’t the parliament and not the King appoint the Governor-General?” If the parliament were to do this, then we would no longer be a constitutional monarchy under the Crown but would become a republic with the politician — controlled state becoming the legal embodiment of executive, legislative, and judicial governance within the country.