The situation in Japan is pretty stable. Why mess with success? And if the emperor has no power, why does it matter if the position is hereditary?
It matters because a hereditary head of state position (actually, any governmental/establishmentarian position) is a terrible symbol in what should be an egalitarian society, no matter if you have political power or not. I don't know how to put this more succinctly.
Why should society be egalitarian? Nature isn't.
Why shouldn't society recognise the heirs of great men specially?
I think that the ideal government has voices for the great mass of the people; for the magnates; and for a monarch. The U.K. system — until Tony Blair destroyed it — was good for exactly this, although the removal of the Lords' ability to block legislation, and the addition of life peers were recent mistakes.
It's a bit more complicated than that, to be fair. A big part of de Gaulle's motivation for the semi-presiential system of the Fifth Republic was due to the instability of the parliamentary system of the Third and Fourth Republics. Whatever else you might say about de Gaulle, the Fifth Republic has been remarkably stable and orderly compared to the regimes that preceded it after the revolution.
Even the same person can see a big difference depending on the popular perception of their power--see Hillary Clinton's favorability rating after she resigned as Secretary of State vs. now when she is running for President.
If Charles, as king, tries to stick his nose in things, he will be unpopular. But if he remains a distant figurehead, I bet he will still be more popular than the elected politicians in Australia.
I'm not intimately familiar with British law, and there may be other reasons why his divorce would make him ineligible, but it would not be for the same reasons that Edward was considered controversial.
Also, as regards Henry VIII and divorce, apparently he used the power of the newly created Church of England to annul his marriages, rather than actually get divorced.
His first wife wasn't giving him male children and she was approaching the end of her childbearing years, so he searched for an excuse to annul his marriage (on the basis it wasn't a valid marriage in the first place). Divorce was out of the question.
When the church administration in Rome didn't support him, he found excuses to break away and found his own church. In fact, the only real difference in the Anglican church in the early years was that Henry was the head of the church instead of the Pope. Anyone who didn't support this view was removed from the church or executed. Later on, the Anglican church evolved in a different direction under more Protestant-minded leaders.
Only two of Henry's marriages were annulled. The very first annulment happened after he had been married for many years and was legally the most questionable. However, he was the law at that point, so he made it happen. The second annulment was more of a typical annulment, and happened when he had only been married for a very short time (a couple months) and was apparently quite uninterested in his new wife.
His second and fifth wives were executed for adultery. The charges were entirely fabricated for Anne Boleyn, but they were probably actually true for Catherine Howard.
The third wife died of natural causes and the sixth wife was still alive and married when Henry died.
So while it may look like Henry made divorce OK for English kings, he technically did not divorce anyone. He either found excuses to have the marriages annulled or they were ended by the deaths of his wives.
I do live in a 1000-year-old constitutional monarchy after all and that's the pro arguments I tend to hear.
"Good for tourism" is another one.
Edward VII played a large role in setting the conditions for the Entente Cordial, in large part by partying a lot in France - activities a politician could never get away with even today. That cultural and ambassadorial role set the scene for the end to a 1000 years of Anglo-French conflict. More recently the current Queen has played major roles in healing the divisions of conflict, most recently with her trip to the Republic of Ireland.
Elderly politicians are still divisive in their election, regardless of whether they're elected by the public or some body. Their actions have to be viewed through the prism of political cynicism and the potential for advancing the interests of their party. Whereas a 90 year old woman who still carries out a punishing schedule of public duties presents a far more inspiring example of duty and loyalty. If no-one voted for you then you are beholden to no-one.
The Australian constitutional referendum was cleverly constructed to keep the monarchy. TWO republican options were offered in order to split the republican side, and both were engineered for short-term aggrandizement of politicians rather than give the country a sound constitution. So a "first, do no harm" strategy ended up with the most votes.
I think a system like the Germans have is pretty reasonable (though more complicated than Australia needs with only a handful of states none with a huge amount of autonomy). Then again, Australia really only needs a head of state to appoint a PM and greet visiting potentates. Apart from that there isn't much need for a GG. Oh and to consume fancy bird feathers.
Like many I chose "The changes on offer are worse than no change at all."
[1]: https://en.wikipedia.org/wiki/Australian_republic_referendum...
At this point, the monarchy is the default position, and I think it will stay that way until the monarch does something to piss off the majority of the Australian people.
Nobody goes to Australia to see the Queen.
Frankly, I think we could do worse then to add some hereditary peers to our republican government.
And generally, one sees that it's been a mistake.
A constitutional monarch can be a good defense against certain types of democratic failure.
As you say, in some countries, the official (purely symbolic) head of state has no real power (pointless in other words). That's OK-ish. I'd rather not have a symbolic president. But the main point is to not make the position hereditary.
Germany's president, whilst largely ceremonial, actually has some (residual) power by the way, but it's a 5-year term. Not elected by the people, however, which is a shame. For example, Finland's president is.