Let's look again:
1Ti 2:1 I exhort therefore, that, first of all, supplications, prayers, intercessions, and giving of thanks, be made for all men;
1Ti 2:2 For kings, and for all that are in authority; that we may lead a quiet and peaceable life in all godliness and honesty.
1Ti 2:3 For this is good and acceptable in the sight of God our Savior;
1Ti 2:4 Who will have all men to be saved, and to come unto the knowledge of the truth.
1Ti 2:5 For there is one God, and one mediator between God and men, the man Christ Jesus;
1Ti 2:6 Who gave himself a ransom for all, to be testified in due time.
Paul says to pray for "all men". He then singles out "kings and those in authority". He sure is singling them out because they are certainly included in the group "all men". Then one sentence later he mentions that only one MAN, Jesus Christ who is a "mediator". There's a very good reason for it...and that is to reinforce the idea that we don't need "kings" or other authorities, or "high priests", to come between us and God anymore. W
Big stretch. Huge.
You're adding to the text the meaning you want to find there.