Q: What is the history of the position of "governor" in the Book of Mormon?
A: It appears suddenly in Alma 2, rather late in the history of the Nephite nation, persists for less than a century, then vanishes for good. The circumstances appear to be the threat of a civil war, led by the Amlicite faction.
No mention of such a position is made in the great governmental reform that replaces a monarchy with judgeships.
The Bible helps us to learn that it is certainly not some 19th century anachronism -- and provides a clue that may solve the mystery of its origin. One of the Old Testament words translated "governor" is "sar," which Strong's concordance also translates as "chief captains."
Go back to Alma 2, verse 13. Facing the Amlicite threat, the Nephites appointed "captains, and chief captains, according to their numbers."
It seems to me that the Nephite governors were not so much politicians as are our modern governors, as they were chief-chief captains, sarim. More akin to the old Roman Republic emergency dictators.