This - excerpted from an essay by Fr Michael Azkoul - seems like an excellent summary of what I think is likely to be true:
THE 20th century has brought an end to sacred monarchy.
To be sure, several nations yet possess a king or queen, but with few exceptions, they reign without ruling. In the West, none of them pretend to hold their position by "the Grace of God," despite the liturgical rhetoric surrounding their coronations. ... nothing is more certain than the disappearance of "sacred kingship" from among so-called Christian nations.
In any case, there has never been a monarch who ruled in the East or in the post-Orthodox West by "the Grace of God," because the existence of true kingship depends upon true faith.
Furthermore, we cannot speak of a heretical society as societas christiana.
The Holy Russian Empire - the last phase of the Roman Imperium, successor to Byzantine or Christian Rome - was the last Christian society and Nicholas II was the last Christian Emperor. His death brought the extinction of "the age of Constantine," the end to God's Plan concerning holy empires.
With the disappearance of Christian Rome, that which restrained world revolution, world atheism, world anarchy, world apostasy, is no more (cf. II Thess. iv, 6).
Secularism characterizes the present age and nowhere is it more obvious than in the principles and policies of the modern democratic state, in which power ascends from the electorate to the elected, to officials and bureaucrats whose only concern, if any at all, is the material and earthly happiness of their constituents.
If there is a place for religion in these "pluralistic societies," it does not inform their attitudes, aspirations and decision-making process. The self-styled "separation of church and state" is a political dogma because it is already a spiritual condition... The secular state is always atheistic.
...The historical evolution of the Western political system from monarchy to democracy is also a process of secularization. By that we mean not only that power was gradually transferred from the ruler to the ruled, the electorate, but also that God and Christian values has come to have less and less influence upon Western life and thought. Power no longer descends from God to His viceroy for the salvation of the people and, of course, the state no longer bears the image of Christ.
The modern political situation is antithetical to that condition which prevailed under the Christian Emperors - or, indeed, under kingship in general. St. Constantine initiated the Christian Roman Empire, the societas christiana in which two ministries, the imperium and sacerdotium, the government and the priesthood, governed one people, a single body politic...
Christian Romans believed they dwelt in an Empire which should encompass the whole world because that Empire was founded on a religion intended for all men.
As a matter of historical fact, the claims of the Empire depended upon the truth of the Christian Faith. The loss of that Faith meant the loss of any claim to the Empire...
The Christian Emperor was not an ordinary ruler. He was vicarius Christi. His coronation was a Sacrament, for he was anointed, as was Saul, David and Solomon, to protect and guide God's People. He was a "messiah," the Saviour, the Spouse of the Bride, the Empire, His Body or, as Professor Kantorwicz puts it, the Empire was his "mystical body," his "second body."...
Also, the coronation of the Basileus or Tzar and the pageantry surrounding it compared to a liturgy. The Patriarch poured oil on his head, a sacramental oil, which signified the king's or emperor's sacred and messianic character, his leadership of God's People. He was the very personification of the "lay priesthood" about which the Apostles spoke.
His position as God's "servant" involved the privilege of entering the sanctuary during the Divine Liturgy to receive the Holy Communion in his hand as was the privilege of the bishop and presbyter. Clearly, then, his authority was not simply political or administrative but spiritual. He was expected to be holy that he might lead his nation into holiness.
He was "the father of his people" whose duties were more than the execution of justice, the prosecution of war and resistance to evil. He was obliged to help the widow and the orphan, to clothe and feed the poor and to defend the Faith. In other words, when he took his coronation oath, he also obliged himself to philanthropia, an imitation of Divine Providence.
On the other hand, the people were expected to obey him as a child obeys his father. No Orthodox spoke of his "rights" - he humbly performed his duties: to God, to the Emperor, to the nation...
...The Orthodox Church has lived with monarchy from the day the Lord established her nearly two thousand years ago. The first monarchy was Roman, sacred and pagan. Of course, some have argued that the Church is "in the world and not of it" and, therefore, it makes little difference what the political structure under which the Church lives; in fact, she ought to have no association with the world whatsoever.
God wished to refuse the Hebrew nation a king and the Orthodox Church is the New Israel. Finally, it would seem that "democracy" would suit Orthodoxy far better than any other form of government, because it is secular. The Church is free to act without the encumbrances of an imperial hierarchy.
First of all, it is important for Orthodoxy to live under a form of government, which is not hostile to Her, even more one, which would encourage Her spiritual and physical growth. The world belongs to Her, as it belongs to Her God. She must, therefore, associate Herself with it in order to sanctify it, to recover it from the Devil.
Thus, when the Lord commanded that all creatures be converted and baptized in the Name of the Father, the Son and the Holy Spirit (Matt xxviii, 18), we must assume that those nations would have governments and that these governments themselves must also become Christian.
It is useless to argue that the Church is "in the world but not of it," because that nation converted to Christ is no longer "of it," no longer "from it."
Consequently, if God hoped to deny the request of the ancient Israelites for a king, it was because He did not wish His People to imitate their neighbors. In any case, they had a government whose ruler was God Himself, directing them with a Law from Above through His appointed Judges - Joshua, Samson, etc.
...If God is King in heaven, he must likewise be King on earth. If all of heaven and earth belong to the Lord, then, similarly the Lord's viceroy is governor of the earth. This explains, in another way, why those not subject to the Orthodox emperors were also heretical and pagan.
Let us say, then, that no Orthodox worth his salt can live comfortably in a society where the Will of God is not accomplished.
How, for example, can we be reconciled to a society in which self-interest is the first principle of all action and where confusion, heresy and skepticism are described as good and creative? How do we share in a government whose authority is human and sometimes deliberately anti-Christian?
One cannot imagine a democracy in which the people humble themselves before the bishop. Worst of all, there is no secular society in which Christ, as a cultural fact, is recognized as God. Moreover, if the state must resemble Christ and the state is secular; then, Christ must he viewed as totally human.
...Thus, it would seem to me that an Orthodox Christian is faced with the dilemma of living in a society which is basically hostile and alien to him. Of course, we must honor the president, obey just laws and do no harm to any man. Yet we cannot allow ourselves to become an intrinsic part of secular society.
The early Christians were accused of being "anti-social" because they would not become involved in the affairs of the pagan Roman Empire, so we must expect the same reproach. Furthermore, we must understand that nothing exists to protect us, no Tzar.
We will be threatened even more with the appearance of the Anti-Christ. He will be the product of secular society. He will, almost ironically, establish a secular monarchy, an ecumenical or world kingship. In the end, of course, he will be overthrown by Christ whose kingdom will have no end.