Mosiah chapter 29 discusses kingship.
King Mosiah II teaches in 29:13 that
If it were possible that you could have just men to be your kings, who would establish the laws of God, and judge this people according to his commandments…then it would be expedient that ye should always have kings to rule over you.
But he ultimately says, “Because all men are not just it is not expedient that ye should have a king or kings to rule over you.” The idea of kings (rather than a single king) to rule over one would indicate some sort of absolute oligarchy, where a very small number of individuals rule as kings, perhaps following the Lamanite model (i.e. Lamoni and his father). In the Lamanite model (see, for instance, Alma 20), it appears different kings ruled over different geographical areas, with one king as ruler over the whole land, and the other kings serving under him.
Mosiah explains and reiterates the plaguing problems with a wicked king:
“How much iniquity doth one wicked king cause to be committed, yea, and what great destruction!”
He brings up the example (fresh in their minds, no doubt) of king Noah, and the resulting bondage and destruction. Mosiah continues in 29:21-23:
“Ye cannot dethrone an iniquitous king save it be through much contention, and the shedding of much blood.”
Why is this? One reason is that he is hard to get to: “For behold, he has his friends in iniquity, and he keepeth his guards about him.”
Under a just set of laws, a ruler might be deposed peacefully. Not in the case of a wicked king. Instead, the wicked ruler destroys past laws (especially the good ones) and makes his own based on his wicked whims. Those who do not obey his laws are destroyed. Mosiah then says, “Thus an unrighteous king doth pervert the ways of all righteousness.” He leads by destruction, by coercion, by compulsion, and at his own whim, rather than following the will of God, or even some shade of godliness such as commonly accepted transcendent principles. Quite the perversion!
And then a summary statement in verse 24: “It is not expedient that such abominations should come upon you.”
He later talks about an accountability issue. He writes:
The sins of many people have been caused by the iniquities of their kings; therefore their iniquities are answered upon the heads of their kings. And now I desire that this inequality should be no more in this land, especially among this my people; but I desire that this land be a land of liberty, and every man may enjoy his rights and privileges alike.
Hence, the problem with wicked kings.
Mosiah also discusses problems with righteous kings, explaining the king’s
“Travails of soul for [his] people, and also all the murmurings of the people to their king…he told them that these things ought not to be; but that the burden should come upon all the people, that every man might bear his part.”
Problems with righteous kings and wicked kings translate to a system of no kings, but one of arbitration (or mediation) by judge. We later read in the Book of Mormon about laws set up by kings (i.e. Alma chapter 1) being followed by the judges. It does not appear that this set of judges had significant legislative ability. Instead, they were granted limited powers of mediation and adjudication, and a corresponding charge to execute the laws already established. We see this in Alma 1 and Alma 30, for instance.
In summary, Mosiah chapter 29 discusses the problems of kingship and concludes that for the Nephite government at the time, a new system of judges would most effectively govern the people.