Interestingly, I can't find any of the same sort of descriptions of what "typing indicators" are from platforms that have implemented them in their chats. It's an affordance that's generated by the system without the user needing to do anything, so maybe that's why there's no information about why they exist. Typing indicators have also been around a while—all the way back to MSN Messenger—so it seems likely that they were mostly adopted as a standard without requiring much justification.