When a baby is swaddled with even one elbow against their body, they do not show this reflex. Once they go to sleep they tend to stay settled longer. In addition to shutting of the moro reflex, swaddling just seems to make some babies more comfortable. Newborns have spent months in tight confines in mom's belly. It is what they are used to. Some babies do not care for the process of being wrapped. I have found that if they are wrapped securly, where they can not move their elbow away from their side, they adjust to the swaddle well.
Swaddling seems to work for most babies during the first three to four months of life. At about four months babies seem to lose the need to be swaddled.