Evil and the Binding of Satan

First, I think it is worth noting that Revelation 20 does not say there will be less evil in the world when Satan is bound. Rather, it says that there will be less demonic deception. Demonic deception is not the main source of evil in the world; fallen mankind is. The specific deception addressed in Revelation 20 is deluding the world into gathering its forces to march against God's people in war.

That is something that used to happen frequently in the Old Testament. God's people were constantly besieged — quite literally — by their enemies. The northern kingdom (Israel) was eventually carried away into exile in 722 B.C., and the southern kingdom (Judah) by Babylon in 536 B.C. Before and after then were many other wars in which nations set out against God's people, killing them, oppressing them, subjugating them, etc.

In the New Testament times, Israel was under Roman rule. In fact, Israel was awaiting a messiah that would free them from this foreign domination, and one reason they rejected Jesus was that he didn't offer them freedom from Rome. Eventually, Rome fairly well crushed the Jewish people (A.D. 70).

But in the wake of Jesus' first advent, the remnant of God's Jewish people and the faithful Gentiles constitute the covenant community of the people of God. Since Jesus' first advent, there have been persecutions, but the level of national warfare leveled against God's people (now the church) has dropped substantially. This is not to say that there have not been national persecutions involving military forces. It is simply to note that the frequency, indeed the constancy, and the breadth of those threats have diminished substantially. What warfare does exist against Christians may be more attributable to human sin than to demonic deception.

Nevertheless, there is a coming day, according to Revelation, when demonic deception may inspire warfare that engulfs God's people on a global level (or not, per historical contingencies). When and if it does, we have the hope that Jesus will return again to save us.