This Nephite government was a new experiment in governing without a king. The reign of the judges was only a generation old, and in the first five years of Alma’s time as chief judge, he had to literally fight Amlici and his followers, who believed they ought to reinstate the kingship. When Alma the Younger departed and his son Helaman took his place, the same problem arose again, leading to a perilous situation which Amalickiah saw as an opportunity.
When the new system was adopted, judges were called by the voice of the people in some type of popular vote. Some Nephites may have believed that anyone who wanted to be elected could put themselves forward as a candidate. However, the system apparently operated most like the way appointees are sustained in the modern church rather than elected by campaigning. That is most likely what King Mosiah intended when he spoke of the role of the “voice of the people.”
This background helps put Amalickiah’s case in perspective. There were many people in this society who could have been dissatisfied with the way things had gone. They were likely unhappy with Helaman telling them that they needed to repent. For an opportunist like Amalickiah, there were religious, political, economic, and personal dissatisfactions which he could use to his advantage. As a Zoramite, he saw his opportunity, and he took it.