An Australian Republic
So, now the Queen is gone many are saying it's time to replace our Head of State with one requiring less pomp and circumstance and more relevant antecedents: by removing the present descendent of Princess Sophia as our monarch and replacing our several 'King's Representatives' with Presidents (or some other title, to address the status of State Governors). In reality, this is already the case. So, let's keep the part 'that sort of works' Then it's simply a matter of amending the several written and implicit Constitutions to provide that these figureheads should be agreed to and installed at regular intervals (currently five years, by convention) by our various Parliaments.
But let's not elect them separately. And when they die let's have a modest memorial, befitting an esteemed citizen.
Travel and life experience has taught me not to support the separate election of Presidents. If it ain't broke don't fix it'.
Electing a President introduces a competing democratic power to elected Parliaments. Competing candidates need to contrive a 'platform' and, by financial necessity and contest, often fund their campaign agenda through hidden patronage, as in the United States.
Throughout the world there are at least a dozen examples of presidents using their initial success and supposed 'mandate' to seize power over the constitutionally established parliament and to install themselves and/or their chosen successors indefinitely. The most glaring examples are Putin in Russia and Xi Jinping in China but the same applies in almost every 'new democracy' in Central Asia, that gained a 'US style' constitution at independence. Even the US itself was recently subject to a coup attempt by a president reluctant to relinquish power.
For the worst example in history, we need only cast our minds back to the Weimar Republic in Germany in 1933, to appreciate the risks that empowering an autocrat entail.
In maintaining Churchill's 'flawed democracy' our leaders should continue to be our democratically elected parliaments alone, because it's the best of: "all those other forms (of government) that have been tried".
Thus, echoing the 1689 the Bill of Rights, our new figurehead needs to continue to be beholding to the Parliament, not an independent power in the land.
In the meantime, we are still a monarchy and so can expect: more ceremonies, pomp and circumstance, and almost certainly, another Royal Visit.