> It is not as if the queen is making these elected governments act in this way.

Not to mention the same class making these gross oversteps of government authority would be the ones to write any republican constitution.

The Queen's representative, the Governor General is the head of a government that is not mitigated by explicit inaliable freedoms that act as a check on it, or divide its powers in a way to prevent it being converted to a classic tyranny. It would require a whole new constitution to remove the powers that these governments have evolved to abuse.

Hence it seems predictable that a popular movement toward new constitutional republics could rise. Without a means to defend your basic freedoms from the people who eventually rise to make up a government, a constitution and a charter of rights are just conventions. These parliamentary democracies are in a co-ordinated transition to something else.

If anything such overreach will lead to a loss of support for republicanism.

As it is I think Australians generally see the Queen (and Governor General to a lesser extent) as being outside politics. There is a deep cynicism in the electorate that it will be possible to select a head of state in a manner that will not be politicised, leading to a loss of independence of the head of state.