The three persons of Father, Son, and Holy Spirit are united in an undivided Trinity, in which all are equal in stature, according to orthodox trinitarian Christianity. Given that our language is linear, it is clear that there are six ways that we could list these three persons. In fact, the order of "Father, Son, and Holy Spirit" is overwhelmingly the dominant one - in the liturgy, especially for baptism (Mt 28:19), in creeds*, and so on. At a distant second is the Son-Father-Spirit order of 2 Corinthians 13:14,
The grace of the Lord Jesus Christ, the love of God, and the communion of the Holy Spirit be with all of you. NRSV
which admittedly sees a lot of liturgical use, though still less than Father-Son-Spirit. I do not think that any other orders are used at all.
Why are other permutations of the three persons not used liturgically? Is there a theological reason why the standard order is the best one (aside from simple Scriptural precedent), or conversely is there some reason (aside from surprise) why a novel order would be wrong?
(I am looking for answers from 'mainstream' trinitarian Christianity.)
* e.g. the Nicene and Athanasian creeds, Reformation confessions (Augsburg, Belgic, Second Helvetic, Thirty-Nine Articles, Westminster), and more recent statements of belief like Baptist Faith and Message