Would you say that the monarchy has anything like the influence of the church these says, Trent? I certainly think not.
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Possibly there is more symbolism attached to the role in England - especially with the monarch being 'Supreme Governor of the CofE'.
However, even in pre-Reformation times, the kings of Scots found it very difficult to assert their role as 'king by divine right'. Probably only three ever managed it to any degree - Alexander III, Robert I and James IV.
The remainder ruled through manipulating the great families - Stewarts, Douglasses, McDonalds, etc, and marrying their offspring, legitimate and illegitimate, into them.
They were, on the whole 'first among equals'.
After the Reformation, Mary Stuart was virtually ignored by her courtiers, and James VI ruled Scotland from afar mainly by committee. He was the last to understand the Scots.
Since then, they/we have treated the institution with a wry scepticism, at times acknowledging, at times reviling it.
The present monarch, Elizabeth I, does her job well - very well.
It's simply that I don't think that there should BE a job for her to do.