Mormon admits the fragility of the Nephite political structure. To review the essential information: the Nephite religious and political system had been a unit until the end of Mosiah2’s reign. Alma1 began establishing churches, and that sub-organization created internal structures that allowed for some separation of religion and politics, a rather remarkable social distinction for that time and place. Mosiah2 continued that division. The unique Nephite religious ideal, which included social equality, continued to dominate politics; but it was neither mandated nor universally accepted and practiced—particularly as time progressed.
At this point in Nephite history, the church coexists throughout the Zarahemla polity with non-church-men. These non-church-men are logically the first whom we would expect to be susceptible to “Lamanite” ideas of social hierarchy. This verse admits that, even within the church, which should be the most zealous stronghold of the Nephite egalitarian idea, some are beginning to toy with alternate possibilities. Since this other way was couched in more political terms, the division between church and state might have tempted them to think they could retain their religion and have a king. After all, they had had kings only two generations earlier.
The flaw in their logic is that the early Nephite kings were decidedly different from the kings in their larger society. Benjamin spells out this difference when he implicitly contrasted himself with them, particularly noting that he supported himself by his own labor. (See commentary accompanying Mosiah 2:10–14.)
A second flaw is that they would not simply be adding a king to their ruling structure but changing their entire social system. They see this attractive system all around them in cities made grand by the labor commanded by those kings and in the nobles who visibly display their wealth. Their own riches are increasing to the point where a similar display of wealth is both possible and desirable. The church-men aren’t necessarily looking for a new religion, but a new socio-political order. What they do not see, and what the prophets saw all too clearly, is that adopting this new social order will destroy Nephite society and, ultimately, the church itself.