In Romans 13:3-4, Paul says that a worldly ruler (arkon) is God's servant. This is often misunderstood, because the contrast that Paul is exposing is missed by commentators who trust political power.
• A judge (exousia) is "God's servant for your good".
• A ruler (arkon) is "God's servant, an avenger for anger".
These are quite different roles. An excellent judge applying God's law provides the only true justice.
God sometimes uses rulers, but not to do good for everyone, because they are not capable of that, but to avenge those who do serious evil. In Romans 12:19, this is a task reserved for God, so his people are not to engage with it. Instead, they must respond to evil with good (Rom 12:17, 21).
In an article about called Prophetic Events, I described the nature of "Protective Judgements".
God sometimes assesses a nation and decides that it has become so evil that it is beyond saving. In this situation, he then has no choice but to allow its destruction to minimise evil. I refer to these as protective judgments, rather than destructive judgments, because their primary purpose is to protect the world from evil. God does not engage in mindless destruction. He always destroys empires when it is the best way to constrain evil.
In the Old Testament environment, prompting one nation to destroy another was often the only way to restrain evil. This did not destroy the evil spirits, but the disruption of war breaks down their uneasy unity and causes them to fight against each. Concentrating in one place allows them to leverage their evil. When evil spirits are dispersed and isolated, they do much less harm.
God uses powerful rulers as his servants. When evil gets out of control through an empire like Rome or Babylon, God often stirs another powerful ruler to destroy it. When the gospel is weak, this is often the best way for him to do it, although he would far rather that the people in the empire came to faith.
Isaiah called Cyrus the Persian God's shepherd and his anointed (messiah) (Is 44:28-45. God used him for two roles. He used him to subdue Darius the Mede, who had defeated Babylon and was getting out of hand and becoming evil. He took hold of Cyrus's "right hand to subdue nations before him and to strip kings of their armour". The right hand symbolises military power. God used Cyrus's military prowess to shift the balance of power in the Middle East.
The second thing that God used Cyrus for was to get the temple rebuilt in Jerusalem (2 Chron 36:22-23; Ezra 1:1).
These verses explain that God moved Cyrus's heart. This is something that the Holy Spirit is skilled at doing. He is clever enough to put an idea into the mind of a ruler that he will like and implement, even though he has not chosen to follow God. Cyrus was superstitious and restored the worship of the local gods in many of the lands that he conquered. Cyrus had not chosen to follow Yahweh, but just wanted to ensure that the gods that controlled Israel were not offended. This is how the Holy Spirit was able to move his heart.
Of course, the Holy Spirit had no problems persuading him to take over the Median empire. Cyrus was a ruthless military leader, so he was eager for that challenge.
Although God called Cyrus his shepherd, he was not a follower of Yahweh. He was a ruthless ruler who controlled a huge empire with brutal force. In turn, Cyrus was controlled by a powerful government-spirit called the Ruler of Persia (Dan 10:13,20).
Cyrus was not interested in establishing the rule of God, but was intent on establishing the strength of his dynasty. He was not interested in serving God, but God was able to use him to achieve a few things that he wanted to achieve at that time.
Cyrus was not a good man that you would submit to in order to become a better person. Two types of people would submit to him. Most of the people within his empire had no choice but to submit to his decrees. They would be beaten if they didn't. Many of them would be slaves, and those who retained their freedom were not much better off. A favoured few would submit to Cyrus to support his rule and share in the benefits of his power. They would have to do everything that he demanded without question. These people served under Cyrus to become rich, not to do good in the world. If they fell out of his favour, they would lose all their wealth and possibly be killed.
Rulers are God's servants, in the sense that God uses them, but that does not mean that followers of Jesus should unreservedly submit to them, because they serve him infrequently and in quite a narrow way by disrupting evil when it gets out of control. The Holy Spirit has to be really clever to get them to do what he wants. He often has to appeal to their baser nature to get them to do his will. Most of the time, they do not serve God, because they reject the voice of the Spirit.
Christians should recognise that rulers will sometimes avenge a great evil. However, they should be very careful about obeying a ruler who is an unreliable servant and who is often controlled by powerful government-spirits.