It should indeed be of serious concern to advocates of monarchy in Britain that the heir to the throne does not appear to know what his job is going to be, despite this being a role he has supposedly been preparing for all of his life. Examples of this are legion but one that stood out to me was hearing him tell one of the Dimbleby brothers that his divorce and remarriage wasn't anyone's business but his own. But he will become titular head of the Church of England so I'm afraid that while many would agree matters like this should be a private matter, they just aren't.
However, those who favour the republican form of government - and I include myself in a half-hearted way - would perhaps do better to recognise the problems that it has had historically and the potential difficulties Britain would have making the transition from constitutional monarchy to this system of government.
We would do better to acknowledge that the record of republics just simply isn't that good. You only have to factor in China and the USSR to see this and there's also the important historical example specific to England that Nick himself cites:
"As so often, hyperbole will hide fear. In this case, the all-too rational fear of monarchists that Charles III will be the best advert the republican cause has had since Charles I."But it is the very case of Charles I that creates problems for British republicans because the previous experiment with it didn't go very well and arguably it is this, along with republicanism's association in people's minds with Irish terrorism, that has made a majority of the British electorate adverse to the British republic.
Perhaps Nick is right to think that Charles will be sufficiently disastrous as a monarch to puncture this previously steady support but another thing I was wondering is - and I'm opening this as a sort of notes and queries exercise - how many countries have made the transition from monarchies to republics without a regime-change? By this we mean governmental collapse after defeat in war, revolution, coup d'etat or independence from an empire or merely a larger political unit. There may be one or two countries that have simply decided to ditch a monarchy but there's not many examples that immediately spring to mind - and it clearly isn't the usual historical path from monarchy to republic.
A number of political scientists - including Juan Linz linked above - have argued that imitation of the American example has been a curse in areas of the world like Latin America because whereas the first priority of the framers of the American constitution was how to limit government, in these places the problem has often been a history of having no properly functioning government to limit in the first place. I suspect many British republicans are also dependent on the American example. It's difficult to know which others, even in the European context, they would be using. Germany and France as they are now perhaps - but we wouldn't have wanted the path to modernity these two took, surely?