There have been previous attempts to change the Nephite government from judges back to a monarchy. To understand those conflicts, and particularly this one, it is important to remember that there was very little distinction between politics and religion in the ancient world, and within the Nephite world view. The creation of churches had allowed some conceptual division, and that may have contributed to the extent of the people who desired different ways, but religion and the right of rule were still connected.
Thus, the kingmen were not only those who wanted a king, but who espoused specific religious ideals, one of which was usually the rejection of the belief in the coming Messiah. Therefore, having a king was not a return to Benjamin and Mosiah, but a return to Zarahemla and a time before there was a Nephite religion in the land.
This is the reason that the opposition to kingmen was freemen. When Chief Captain Moroni raised the title of liberty, it was a declaration of religious liberty, not specifically political freedoms. Thus, it is that the freedom desired by the freemen was not particular political rights, but the ability to continue to worship as they desired. The conflict is identified by the difference between the rule of a king or the judges, but the deeper conflict was the religious understanding of the people. The type of kingship that the kingmen espoused would lead to the destruction of the Nephite understanding of Mosaic religion combined with the prophecies of the coming of the Messiah.