"...for kings and all those in authority, that we may live peaceful and quiet lives in all godliness and holiness." 1 Tim. 2:2
Why does Paul say this? Because it "pleases God our Savior, who wants ALL MEN to be saved and to come to a knowledge of the truth" (v.3-4).
How often this second verse and its necessary connection to the first has been overlooked!! Paul is basically saying this: Pray for leaders; God wants them to be saved, and if they are saved they will be sure to use their authority to bring peace to the Christians. Why else would Paul go to the trouble of attaching to his prayer exhortation a theological description of God's salvific purposes? The movement of thought is very plain.