In ST III.35.7, St. Thomas considers why Our Lord was born in Bethlehem. Obj 3 argues that Christ should have been born in Rome, which at the time ruled the world, since from there he could have more easily made known to the whole world the true faith:
The Lord was born in the world for this, that he might announce the faith of truth . . . but this would have been able to have come about more easily if he had been born in the Roman city, which then was having dominion of the globe . . . therefore it seems that he ought not to have been born in Bethlehem.
In response, the Angelic Doctor quotes a sermon from the Council of Ephesus, which argues that, if Christ had chosen as his birthplace the great city of Rome, the change of the world which the Christian Faith accomplished would have been ascribed to the power and influence of Rome. Similarly, if he had chosen to be born the son of an emperor, his benefit to the world would have been ascribed to the power and influence of the emperor. But “so that divinity would be known to have transformed the globe, he chose a poor mother and a poorer birthplace.”
Then, however, Saint Thomas points to 1 Corinthians 1:27, which reads: “But the weak things of the world God hath chosen, that He may confound the strong.” From this he concludes:
Therefore, so that he might more show his own power, in Rome itself, which was the head of the globe, he established the head of his Church, in sign of his perfect victory, so that thence the faith would be dispersed to the whole world . . .
In short, Our Lord chose Bethlehem as his birthplace so no one could ascribe his victory to the earthly power of his origins; but he chose Rome as the head of his Church, so that the extent of his victory would be total and undeniable. Rome was the capitol of the world, so it was fitting that it should become the capitol of the Church, that the Church’s triumph over the world could be more clearly evident.