These verses become more poignant when we realize that they describe the recent past. This is not a generalized comment about the promise of the land. Benjamin is discussing what has recently happened. Benjamin declares that their recent victory follows the evidence of the past where Jehovah had preserved the Nephites. Had Jehovah not fulfilled his part of the covenant of the land’s promise, then the Lamanites would surely have been victorious.
On the heels of his statement that he would give the people a new name (from verse 11) this discussion of what would happen if the Nephites were not righteous becomes the reason that the new name is desirable. The division had led to contention and therefore unrighteousness. With a new name, they could become a new people and therefore be one. If they are one people, there will not be internal divisions. If that new name is accompanied by a rededication to follow the commandments, then they would not have the temptation to become weak as part of their own society, rather than only the world around them.