Catholic monarchist Charles Coulombe also addresses this issue in his Monarchy FAQ:
But wasn‘t God angry at the people of Israel for wanting a King? Weren‘t Judges better?
The Judges of Israel were directly called by God, with neither acclamation by the people nor constitutional restraint. The fallen nature of the Israelites made such a government unfeasible for long---did not Our Lord complain that Jerusalem murdered the prophets? Having been chosen from all the Earth, the Israelites ought to been gratified that they had been given such a unique---and to our way of thinking, undemocratic---system of government. Instead, they demanded the natural manner of rule enjoyed by all other peoples---hence God‘s anger. But He nevertheless showed His approval of the institution both by having Samuel anoint Saul, and by establishing the dynasty of King David, whose last rightful heir according to the flesh, Jesus Christ, continues to rule by right over us all, whether we wish Him or not. It is by Him, and as a reflection of Him, that, as Pope Pius XI‘s hymn to Christ the King puts it, "Kings the Crown and Sceptre hold," as pledge of His supremacy.
In any case, the Judgeship is completely irrelevant to us to-day. Our republic is certainly nothing like it, and one cannot imagine whom God might choose to rule a heathen people like the Americans. (It is interesting that no such thing has ever happened in Catholic countries). Did we attempt such a thing, we would doubtless have a regime like the Mormons did in pre-Territorial Utah, or the colonists in New Haven, where the ministers would run things. One can imagine what the result would be. Such non-Catholic clerics would have the power of life and death over all citizens, Catholic or not --- and no constitutional or legal restraints on them. Even a non-Christian Monarchy, restrained by local traditions, would be far preferable.
I'd like to add: how can Christ be "King of Kings" if there are no earthly Kings for him to be King of? He is not "King of Presidents" or "President of Presidents."
That one section of Samuel explains why the monarchy and their collaborators in the Roman Church were so desperate to keep the scriptures out of the hands of the commons. It is a knife into the heart of the self-serving lie that monarchy, not liberty, is God’s perfect will for man.