Dr Eamonn Butler of the Adam Smith Institute gets it:
As titular head of the government, the army and the judiciary, the Queen notionally has the power to prevent these institutions being perverted by anti-democratic tyrants. It is not the power that the Queen wields, but the power that she, in theory, denies others. In fact, the present Queen has not done enough to prevent politicians over-expanding their power; but over the centuries, the system has definitely had some positive effect.
There is no point in a constitutional monarchy for its own sake. The point, as the (classical) liberal Butler here and Dr Sean Gabb of the Libertarian Alliance both realise, is that it’s the best way we know of safeguarding our liberties against tyranny. In this it has been pretty successful and even the long reign of the worst and most negligent monarch in our history has not – at least yet – snuffed them out entirely. That we live in relatively benign society does not mean this will always be the case. Queen Elizabeth II or one of her successors may be truly tested one day in the same way that Spain’s King Juan Carlos was tested in 1981 when he faced down a military coup. If that day should come we should expect our monarch to break a habit and do the same. This would be the very point of their existence.
Americans might be interested in Butler’s subsequent comment on the path of their own (elected) monarch.