A speaker may have very little time, be facing a rapidly changing event, or need to avoid verbal length that obstructs urgent communication. Ellipsis can then serve brevity under situational pressure (ضيق المقام). This motive differs from testing the listener's intelligence.
If everyone is watching one endangered person and a witness cries «نَاجٍ!»—“[He is] safe!”—the intended subject may be instantly clear without a name.
But where several people are involved, the same cry might cause confusion about who survived. The rhetorically appropriate form balances the need for speed with the need for reliable identification; brevity alone is not the criterion.