It's mostly about the user experience of the follower, I think (more than the fact that the stories go away after 24 hours).

Snapchat allows a follower to consume all of the stories that they follow in a single stream. You only have to tap quickly to go to the next media item. One can also skip one story and move on to the next with a single swipe.

The fact that everything has to be a direct photo or video from a phone also makes every story feel less manufactured and more genuine. For example, I can go to an NBA player's Twitter account and find that personal tweets and messages from their sponsors are completely mixed in a single feed, while their Snapchat feed is all about their day-to-day personal life (which some find much more interesting).