I added a link to his original post to your comment, Alex.
The immediate practical result expected from praying for kings and all those in a superior place, is “that we may be leading a mild and quiet life in every devoutness and gravity”: so as a practical matter Paul was exhorting them to pray for those particular individuals reigning over them at the moment (who, as tyrant pagan oppressors, would be in a position to make their lives much less mild and quiet!), not only for “kings” as an abstract group.
Since there might be resentment about the idea of praying for kings and superiors, Paul adds the greater rationale that “our Savior, God, wills all persons be saved and come into a realization of the truth”. To this Paul appends a brief kerygma (presumably well-known to the church already) about Christ being the mediator of God and man, the One giving Himself as a correspondent ransom over the same all. (English translations tend to render that “for all”, which is also true, but the Greek is “over all”, which connects to the authority and position of God over all, including over those kings and superiors.)
So the all persons are inclusive as a group, and also particular: even all kings (whoever they are), including the particular ones who can make our lives miserable or quiet and peaceful. The concept of both all kinds and all particulars is embedded in the phraseology “over all”, which is actually plural in Greek “over alls”, in a statement of the superiority of Christ: Christ is not superior only over all kinds of people, but over all persons individually (save the Father alone of course).
Moreover, most non-universalistic soteriologies, whether Calv or Arm variants, acknowledge that God’s will shall certainly be done here in regard to half of this prayer: all persons (not only all kinds of persons, and not even only all human persons!) shall come to realize the truth. But then, if this realization of the truth (which Paul connects directly to salvation from sin) shall be certainly accomplished, and if God also wills that salvation shall be accomplished, and if (as Paul continues immediately afterward by saying) Christ is a ransom over all (plural) for the accomplishment of salvation–then it seems like a very broken theology to deny that God will surely succeed in one such important deed while failing (or never even trying) on the other!