The voice of the people does perhaps become more important in the reign of the judges because it becomes a method for the removal of an unrighteous judge. Mosiah had indicated that it was difficult to remove an unrighteous king without bloodshed, and it is that context that provides the background to this part of his instructions. The people typically desire that which is right, therefore they would support righteous judges.
Nevertheless, it is possible that the people would not desire righteousness. That can occur, but that is a case of apostasy and will invoke the negative aspect of the promise of the land. When the people are no longer righteous, they not only lose their divine protection, but will be visited with destruction.
The method of removal is to be orderly, however. A judge who does not judge according to established law would be brought to a higher judge. Even the higher judge could be removed with the combined judgments of lower judges. Thus, there is an established way that the people could remove an unrighteous judge without resorting to bloodshed.