Well, as a Catholic (now moving into the Orthodox faith), I do believe in Monarchs ruling because God put them there but that doesn't mean that my fellow countrymen believe the same and even some people who follow the same religious principles as I do, won't believe in "Divine Right". Britain is slowly becoming more like Scandinavai, in that, we're starting the process of becoming a secular nation that encourages multi-faith communities. But as you say, Britain likes tradition. The wider world is changing and in many ways, I think Britain is split with one half wanting us to change with it and the other half wanting us to slow down and take things slowly.
The Church of England no longer has the same reverance from people or the power it once enjoyed because it's gone down the popularity path. Lord Carey, the old Archbishop of Canterbury, said when he stepped down that the Church shouldn't change it's views to get more people into the churches. Sadly, thats what it has done and Charles has criticised the Church of England for doing just that. But in other ways, he's been treated very well by the Church. The Archbishop of Canterbury carried out the wedding blessing etc and in many ways, Charles and the Archbishop agree on matters spiritual. Rowan Williams recently said that the Churches should go "back to the Eastern founding fathers of our faith". And that matches with Charles's faith and his fondness for Orthodoxy.
I think that Britain has two roads to go down and it will be Charles's time as Sovereign that sees the choice made. We can follow the path of America and say, we're now a secular republic or we can follow the path of Norway, where we have a Monarchy and there are religious affiliations but they aren't raised above any other religion. So, the key really will be the two leaders of the time. Personally, I believe that if it's a Labour Prime Minister and Charles, a republic could become more likely. If it's a Conversative Prime Minister (namely David Cameron), then it'll be the Norwegian route we follow.
I think that Britain would keep the coronation ceremony because it's just something we've always done. An investiture just wouldn't be British, but I suppose it could work. It's the anointing with oil thing that could be a problem but that raises the question, "What makes a King a King?" and thats where alot of Britons worry because it means reassessing alot more than just the Monarchy. It would mean the total evaluation of the establishment, the way we live and the society we've built. And I see it as slightly dangerous to make big changes to something we can't get back once it's gone.
It's certainly going to be interesting to see how things pan out. Thanks for your compliments on my posts. I'm glad you like them.