Probably to maintain the spontaneity and freshness of the shared moments. It prevents people from re-watching and over-analyzing, keeping it more like real-life interactions. Also, it might encourage users to share more unique and timely content knowing it won't be replayed repeatedly.
The reason could be that Snapchat aims to replicate the real-time, ephemeral nature of communication. By allowing only one view, it makes the stories feel more immediate and special. It also reduces the potential for saved or shared content outside of the app's intended context.