In a politicians’ republic, many more of the positions in the state are reserved for the political class. These certainly include the head of state, his deputy, and where these exist, state or provincial governors and lieutenant governors. They may include the public service. (Bagehot thought only a constitutional monarchy could assure an independent public service.)
In some politicians’ republics even the judges and the army can be filled by the political class.
I am always fascinated by the way the President of France, who plays a significant executive role witha subordinate prime minister, delivers the New Year message. French republicanism being against religion, at times violently so, this is not delivered at Christmas.
This is now presented very early in the main evening news as " The Wishes of Monsieur The President of The Republic." It is preceded by some formal scene, in the past the facade of the Presidential Palace, while The Marseillaise is played. ( The Marseillaise is a stirring anthem written by a royalist for a France which was then, briefly, a constitutional monarchy.)
The President now delivers an address for about eight or nine minutes – it used to be longer. These days he stands; once he was seated on what looked like a golden throne, sometimes with or without a gilt desk.
It is invariably a thinly veiled political message about the government.
This is completely unlike The Queen’s which is of course beyond politics.
But that is how our sophisticated and advanced crowned republics function. The Crown – Australian, Canadian, New Zealand, Spanish, Dutch etc. – is above politics.