John Calvin comments on 1 Timothy 2.2 (boldface added):
For kings He expressly mentions kings and other magistrates because, more than all others, they might be hated by Christians. All the magistrates who existed at that time were so many sworn enemies of Christ; and therefore this thought might occur to them, that they ought not to pray for those who devoted all their power and all their wealth to fight against the kingdom of Christ, the extension of which is above all things desirable. The apostle meets this difficulty, and expressly enjoins Christians to pray for them also. And, indeed, the depravity of men is not a reason why God’s ordinance should not be loved. Accordingly, seeing that God appointed magistrates and princes for the preservation of mankind, however much they fall short of the divine appointment, still we must not on that account cease to love what belongs to God, and to desire that it may remain in force. That is the reason why believers, in whatever country they live, must not only obey the laws and the government of magistrates, but likewise in their prayers supplicate God for their salvation. Jeremiah said to the Israelites,
“Pray for the peace of Babylon, for in their peace ye shall have peace.” (Jeremiah 29:7.)
The universal doctrine is this, that we should desire the continuance and peaceful condition of those governments which have been appointed by God.
Or consider Calvin’s comments on Psalm 72.11 (boldface added):
And all kings shall prostrate themselves before him. This verse contains a more distinct statement of the truth, That the whole world will be brought in subjection to the authority of Christ. The kingdom of Judah was unquestionably never more flourishing than under the reign of Solomon; but even then there were only a small number of kings who paid tribute to him, and what they paid was inconsiderable in amount; and, moreover, it was paid upon condition that they should be allowed to live in the enjoyment of liberty under their own laws. While David then began with his own son, and the posterity of his son, he rose by the Spirit of prophecy to the spiritual kingdom of Christ; a point worthy of our special notice, since it teaches us that we have not been called to the hope of everlasting salvation by chance, but because our heavenly Father had already destined to give us to his Son. From this we also learn, that in the Church and flock of Christ there is a place for kings; whom David does not here disarm of their sword nor despoil of their crown, in order to admit them into the Church, but rather declares that they will come with all the dignity of their station to prostrate themselves at the feet of Christ.
In my opinion, the fact that the Institutes are appeals to a king should settle the matter…