Sir Winston Churchill is credited with the remark that the British style of government is the worst system in the world, except for all the others. I'm not sure he actually said it, but whoever did had a point.

As I see it, any effort to do away with the role of the constitutional monarch is stymied by the prospect of problems that are even worse than the ideologically distasteful (to some) situation of being a citizen of state headed by a aristocrat who rules by right of inheritance.