The sakkos entered the church from the palace. It began as a garment of the Byzantine emperors, and it was given, as an honour, to the patriarch of Constantinople, who at first wore it only on the greatest feasts of the year. From there it moved outward and downward in the ordinary manner of court privileges: to the other patriarchs, then to certain metropolitans as a personal grant, then to metropolitans generally, and by the seventeenth century to every bishop of the Byzantine rite.
What it displaced tells the same story from the other side. The older episcopal vestment was the phelonion, and specifically the polystavrion, the phelonion covered with crosses, which was what a bishop wore before the sakkos arrived. As the sakkos spread the phelonion settled downward to become the vestment of a priest, which is what it is today. Two garments changed places over several centuries and neither change was ever legislated in one act.
The result is a vestment whose history is a record of an empire's honours passing into ecclesiastical use and then outliving the empire entirely. Every Orthodox bishop in the world now wears, as the ordinary mark of his order, a robe that was once a gift from a Christian emperor to one particular bishop as a mark of favour.