In 1539, Pope Paul III explained that this devotion is "to appease the anger of God, provoked by the offences of Christians, and in order to bring to naught the efforts and machinations of the Turks, who are pressing forward to the destruction of Christendom" And in 1592, when regulating the Forty Hours Prayer for the City, Pope Clement VIII (known for his Vulgate, his Index, and his conversion of Henry IV of France) wrote: "Pray for the Holy Catholic Church, that the mists of error may be scattered and the truth of the one Faith be diffused throughout the world ... pray that the enemies of our Faith, the dreaded Turks, who in the heat of their presumptuous fury, threaten slavery and devastation to all Christendom, may be crushed by the right hand of the Almighty ...".
The atomised individualism of the Enlightenment still, perhaps, prevents us from discerning the importance and power of such intercessory and expiatory prayer. Let me unpack it a little.
The Creator might not have created.
When He created, He might just have created one single monadic Time and Place and Being.
Instead, it was His will and nature to create an immense and interlocking complexity of times and places and beings.
He situated in this Creation an even more complex interaction of causes and effects. He thus placed Causality in His creation as perhaps its most important feature.
So intercessory and expiatory prayer is not an attempt to twist God's arm or hubristically to achieve a result outside His will.
Instead, it is His wonderful gift of the opportunity of entering into His will; of sharing His own causality.
Think about it: what more could a Creatot give?
This is why S Paul (I Cor 3:9) can call us sunergoi (fellow-workers) of God, and can so blithely, so naturally claim that he himself in his flesh completes what is lacking (!!!) in Christ's afflictions for the sake of His Body, that is, the Church (Col 1; 24).
By the way ... by papal disposition, the dominant vocal Prayer during the Quarant'Ore is the Litanies. Not the devotional litanies, admirable as they are in themselves, but the great, majestic austere formula that we call the Litanies of the Saints, because it brings alongside ourselves all those others who share so willingly with us in our sunergeia with our Maker.
A sharing in the merits of our Lord Jesus Christ and of all his Saints is affirmed by the Indulgences in the current Handbook: Plenary for those who visit the Most Holy Sacrament in order to adore It for at least half an hour; Partial for those who devoutly recite the Litanies.