Since God allows Satan to exist, why should we pray for him to be crushed?

As the prayer begins: "defend us in battle". So it is an intercessional prayer to seek the protection of the leader of God's army of angels.

St. Paul exhorts:

"For we are not contending against flesh and blood, but against the principalities, against the powers, against the world rulers of this present darkness, against the spiritual hosts of wickedness in the heavenly places." (Ephesians 6:12)

This means that our constant struggle in life against evil is actually against Satan and the demons who followed him, who resit God, his saints and angels. So we do not merely pray for Satan to be crushed, but we pray for God to protect us from him "do not lead us into temptation".

This prayer to St. Michael the Archangel is a fascinating study in the internal contradictions and logical acrobatics that characterize much of religious thought. The prayer asks for God to thrust Satan into hell, which implies that Satan is currently not in hell and is free to cause havoc in the world. This raises the question, why would an omnipotent, benevolent deity allow such a malevolent being to exist and exert influence in the first place?

The theologian's answer might be that God allows Satan to roam as a test of faith for humans, or as a consequence of granting free will. But these are unsatisfactory explanations. The idea that an all-good God would permit such evil for the sake of a 'test' borders on the sadistic. As for free will, it hardly seems free if it comes with the threat of eternal torment for making the wrong choices.

This prayer, like many religious texts, reflects a struggle to reconcile a world filled with suffering and evil with the belief in a just and loving God. It's a testament to our human capacity for cognitive dissonance, our ability to hold two fundamentally contradictory ideas in our head at the same time and somehow continue to function.

So why does the Pope pray for God to thrust Satan into hell? Because that's the narrative that has been constructed: a cosmic battle between good and evil, in which humans can appeal for divine intervention. But it's all a grand spectacle, a drama played out in the human imagination, not an objective reality.

Since God allows Satan to exist, why should we pray for him to be crushed?

Satan is known as the Father of Lies and the archenemy of God.

As such the children of God must pray the the kingdom of Satan be destroyed and the Kingdom of God be restored here upon earth.

For some mysterious reason God allows Satan and some of the evil spirits to roam the earth in order to tempt mankind into sinning.

From the Blog of Archdiocese of Washington:

Thus, though consigned to Hell, it would seem that some or all of the demons have the ability to roam the earth as well. Demons, however, do not have bodies and thus do not “roam the earth” the way we do. Their “roaming” is more an indication of their capacity to influence than their ability to move from one place to another. Further, Satan and demons are described as being “chained,” “in prison,” or “in darkness.” This is likely a way of indicating that their power to influence or “roam” is limited in some way. This does not say that they do not wield considerable power, just that it is not unbounded. If you think it is bad now, just imagine what it will be like when their power is unchained! - You can read more about it here

Do not forget that Satan tempted Jesus in the Desert. Now if if Christ was tempted by the Demon, then it is plainly obvious that we too will tempted in mysterious ways by the Devil.

Some exorcists commands demons to go back to hell.

St. Peter (1 Peter 5:8-9) exhorts us to be careful in regards to the Devil.

8 Be sober and watch: because your adversary the Devil, as a roaring lion, goeth about seeking whom he may devour.

9 Whom resist ye, strong in faith: knowing that the same affliction befalls your brethren who are in the world.

The pope as the successor of St. Peter is stating the same message.

One does not need to be a Catholic in order to pray for God to crush Satan! Anybody who reads the Bible and who has spotted the first prophecy (in Genesis 3:15) will know that God has promised to crush him in the head! Further, if they have read on into the New Testament, they will know at what stage that prophecy is, in its being worked out, in time.

All Bible believers know that Satan was to be allowed to bruise the seed of God's 'woman' in the heel, and that that happened at the cross of Christ. They will also be encouraged knowing that Christ's resurrection and ascension to heaven marked the casting of Satan and his demons out of heaven (Revelation 12:7-13), to be restricted until the final stage, when they are cast into the lake of fire "the second death" to be tormented forever (Revelation - various verses.) Note: as hell is the final thing to be cast into this lake of fire, which Satan and the demons are already in, it cannot be hell, as your question implies.

As that final stage does not happen until Christ's spectacular return to Earth to usher in the Day of Resurrection and Judgment, and we await that event, all Christians pray as did the apostle John (who wrote down that Revelation), "Amen. Even so, come Lord Jesus." (Rev. 21:20) That is equally a prayer for Satan to be crushed as it is for Christ to return. That prayer has been on the lips of Christians from when John first prayed it, until today. We know what will happen, but we do not know when it will happen. So, we pray on, in faith, knowing it will happen because God has promised, and we believe the promises of God. Christians were told by the apostle Peter that they should live in faith, looking for what will yet come, praying for things to come, in the sense of "hastening" their coming at "the day of the Lord" (2 Peter 3:12).

Such prayers of faith constitute a request, not a demand. We are expressing agreement with God's stated will. That is why Christians pray for Satan to be crushed.