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.