absurdity of being a Constitutional Monarchy

While it appears that Australians are completely comfortable with Australia remaining a Constitutional Monarchy and not becoming a Republic, what really riles me up is the insidious practice of creating a fiction to show that we're already an independent country with no legal ties (in reality) to the old country. Oh really? Well without rehashing the whole Republic debate here (the for and against arguments have been done to death over the last 15-20 years), I will just say that the Governor-General is NOT our Head of State, he is the Queen's Viceroy (as I call him), or if you prefer the correct description (as stated on my passport) "the Governor-General of the Commonwealth of Australia, being the representative in Australia of Her Majesty Queen Elizabeth the Second". The G-G does NOT receive the full class A diplomatic recognition as the Head of State, indeed he/she gets the B treatment as a mere "representative" of the TRUE  Head of State, our glorious benevolent Queen.
But if you think this is no big deal (in reality), what would happen then should the US ask us to be part of a "coalition of the willing" to invade a Commonwealth Country? Sound fanciful? It may've been airbrushed from the public consciousness, but the US invaded Grenada in 1983 (to the public disgust of the Thatcher Govt). The Queen is the "Commander and Chief" of the Australian armed forces, yet we would be invading ourselves under this scenario.
There's so many of these types of scenarios I could point to which show how ridiculous Australia being a Constitutional Monarchy truly is, but is there anything more absurd than invading yourself?