A referendum would also be a bit of a nightmare globally surely? If we voted to get rid of the monarchy, presumably we wouldn’t be doing that on behalf of other countries. I mean, I’m sure they’d probably follow suit due to the practicalities (can you have a king of Canada, Australia etc living in the UK but not funded by the UK and not king of the Uk - how would it work) but some, not all, might be a bit annoyed, with a sense from the various prime ministers of “actually now is not a great time for us to be rewriting our constitution, we’re a bit busy, so thanks for chucking this at me. A huge row over what sort of power structure we have at the top of government is just what I wanted”.
I’m Australian and while I think some Australians would be sad to see the King go as head of state, he’s really not got any power here now. The King of Australia is a figurehead only.
Although the King’s representative in Australia is the Australian Governor General - she is appointed by the Australian government and answers only to the Australian government. The monarch has no power and no influence here, although he is kept informed. He is not head of our armed forces either.
But I agree that the above poster is right in that it wouldn’t be that welcomed at this time. I don’t think there are many people really looking to change head of state at the moment. I do think if America had elected a more stable president then we would have had a referendum to change our head of state sometime in the next three years. It’s currently off the table. If the current Australian government gets a third term in 3 years time, there’d be any huge row over what form of president we have.
I doubt there’d be any ‘huge row’ though. If the King stood down, the decision of whether to have a republic is made for us. It would then be a question of do we want an elected president or do we want a president appointed by the government? We see what is happening under Trump. He looks to be in mental decline just as Biden seemed to be by the end of his term. I suspect most of us would be inclined to think a President appointed by the Australian government, who can be dismissed by the government, is the best way to go.