Does anyone know why Satan is allowed to rule this worldly system?

Satan doesn't exist. Don't buy into any of the control nonsense -- it is all based on mythical figures.

Satan USED TO RULE the earth.

Jesus rules now.

Only fools continue to follow Satan and swallow his lies.

when satan was cast out of heaven after Jesus died a sinless life, he lost all his power except ONE: temptation. Now, all he can do is tempt. And he has perfected that power to the utmost. All the evil in the world is perpetrated because the perpetrator falls for temptation: sexual crimes, property crimes, bodily crimes against persons and against nations, all driven by evil inclinations to own more, have more, hurt others more to benefit oneself, and get get and get. So satan rules the worldly system by his own mashinations - tempting people to do evil, and when they do evil, they fall under his domination and power.

When Adam fell in the garden, it was by satan tempting him to do that which God said was forbidden. So from day 6 of world history, satan prevailed on earth and was given access to heaven, where he stood before God like a prosecutor, accusing those who died who appeared in their souls before God, of sinning. Like only one boxer can be the heavyweight champion, when satan defeated Adam by the trick of temptation, satan occupied the role of power in this world like the heavyweight champion of the world has. Someone must come along, succeed in resisting temptation, and die a sinless life. When such a person succeeds at that, then satan will be cast out of heaven, lose his power to appear before God and accuse (read the book of Zechariah in the OT and in Job). So when Jesus came, satan saw the danger to his power. He didn't tempt Jesus with a piece of fruit, like he succeeded in tempting Adam, he tempted Jesus by offering him THE ENTIRE WORLD and all its peoples and nations, if Jesus would worship him. But Jesus withstood the temptation and refused, telling satan "thou shalt worship only the Lord God". So satan had his back to the wall. He faced a dilemma,= if Jesus would remain alive, and live the perfect sinless life, then the kingdom of God would come on earth because satan would be dethroned as prince of this world. But if Jesus died then that would not come to be, and Jesus would be out of the way, (so satan thought). So he tempted Judas to betray Jesus and succeded at that. He thought then the kingdom of God would not come, but he didnt realize that living a sinless life and giving his own blood and body as a blood sacrifice for the sins of the whole world, would affect satan. But when Jesus died on the cross, satan was cast out of heaven, left limited to this eart, unable to appear before God and accuse newly deceased sould appearing before God of their sins, as Jesus rose to heaven to occupy the place satan had, and instead of accusing others who come before God's throne, Jesus intercedes for repentent sinners to obtain God's grace for the forgiveness of their sins.

So that;s how satan rules the world's system, where he is not confined - by temptation, like he tempted Adam to commit a wrongful act, like he tempted Judas, he tempts men today while controlling their minds, to act as they do to get and use power.

because adam sold it to him for a bite of fruit.

Read the Bible. It is all there.