I think that what the Queen exemplifies for many people is the sense of doing her duty. She turns up wherever she’s needed, and mostly does the job pretty well. There’s not really been any scandal attached to her.
I think she’s always followed the example laid down by her parents, to the extent that nothing much seems to have changed since their day. I don’t know how she reconciles the notion of her position being God-given, since presumably that makes God responsible for Edward doing a bunk with his lady-love, and landing her father with the job which probably precipitated his early death. I’m not sure that she’s ever done much in the way of independent thinking. The Palace Mandarins must bless her for that, and are probably not looking forward to serving the next Monarch.
I do agree with BertrandRussell that it’s all about the institution, and the continuance thereof. I don’t think it’s just about the careers of the Palace courtiers, it’s the mindset that goes along with taking on that kind of job in the first place. Supporting the continuance of the institution isn’t too difficult if the major players are fulfilling their roles, but there have been quite a number of junior members over many decades who have taken advantage of their privilege. If Charles does get to reign, it’ll be a short reign, and he’ll mostly be able to rely on the memory of his mother to see him through. Of the rest, I think it’s mostly the women who have married in, especially Kate, who are the RF’s best bet.
The problem with removing the monarch as head of state is that so much of our laws and institutions are tied in with that. And I don’t think any Prime Minister would want to be in the history books for being the one in charge in that event.