It's worth noting that Augustine's statement that Rome never was a true republic takes place *after* the emperors have embraced Christianity. This is just one more piece of evidence that an integralist reading of the City of God is totally untenable.

In fact, he thinks Rome was closer to being a republic, closer to having true justice, in ancient times, before it was officially Christian, than in "modern" times.

Of course it wasn't even then, but this shows how conversion of rulers or even official recognition of right worship don't = legitimacy, or even automatically superiority over more overtly pagan regimes. (Which isn't to say Augustine thinks such conversion or recognition is bad)

But a regime which is truly Christian will be one which follows the demands of justice even to the point of allowing itself to perish rather than preserving itself through injustice, and there hasn't ever been a republic or empire which met this standard.

When he praises the Christian emperor in book V (whatever we think of this), he praises him for humility, sharing power, being willing to repent in humiliating penitence for atrocities, for everything that is the opposite of glorious integralist triumphalism

True worship is the foundation of true justice, but the integralists are wrong to invert this into: public recognition of true worship is the "solution." Whereas Augustine seems to shift the focus to the heavenly city as the only solution, even if a Christian ruler might be nice

Augustine is interested in defending Christianity against the accusation that the rejection of the cult of the Roman gods and the advent of Christian worship caused the downfall of Rome, but this does not require him to defend the empire as a Christian regime or a genuine polity