As I understand it, the Oath of Allegiance, to which all military personnel swear, is to the Queen, and not to any government. So it is a sort of fail safe, which, in theory, precludes a government controlling the military. (??? Afghanistan?!) Does it work?
In a way, the principle is a good one, but in a written, democratic constitution, the Head of State need not be a person of accidental, hereditary privilege and wealth, but one chosen by the people.
The pageantry is fun and interesting, but also emotive, given its links. It could be kept alive in an historical events calendar.
Democracy means that those who have more should not have the immediate right to dictate to those who have less. Wealth does not mandate power. (CF CofE, RC church, etc. etc. but that's another issue.