The Book of Mormon records the history of several righteous kings. Nephi, Benjamin, Mosiah, and others led the Nephites in righteousness. When the king is a righteous as these men were, a monarchial form of government is even more efficient than a democracy. The latter has built-in inefficiency and checks and balances. The former allows the righteous king to do the right thing immediately, without waiting for legislative funding, constitutional conformity, or public approval. Accordingly, during the Millenium, the righteous will be ruled by a monarchial theocracy with the Lord as “Prophet, Priest, and King” (Hymn #136).
The problem with continuing under a monarchy, then, is that these righteous men are exceptional. The general rule is that less righteous, or frankly wicked, men eventually rise to power only to make the people suffer thereby. As Mosiah says, because all men are not just it is not expedient that ye should have a king or kings to rule over you (v. 16). Therefore, the prophets were always leery of establishing a government of kings. Nephi was faced with a people who looked up to them as their leader, And it came to pass that they would that I should be their king. But I, Nephi, was desirous that they should have no king; nevertheless, I did for them according to that which was in my power (2 Nephi 5:18). In the Old Testament, we read that when the Israelites asked the prophet Samuel for a king so that they could be like all the other nations in the land, the Lord replied, Hearken unto the voice of the people…for they have not rejected thee, but they have rejected me, that I should not reign over them (1 Sam 8:7). The Israelites would have benefited most if they had the KING OF KINGS, AND LORD OF LORDS (Rev 19:16) as their king, for I, the Lord, the king of heaven, will be their king, and I will be a light unto them forever, that hear my words (2 Nephi 10:14).