It would be advantageous if we had more event driven bots, such as a weather bot proactively notifying us about a storm approaching so we could close the windows. Also imagine a game matchmaking bot that observed the presence of people in groups and propose to have a match when it sees a sufficient number of people who had played the given game in the past are around at the same time.
A related question is how to schedule actions and messages in general, and that could be approximated client side, solved elegantly via a chatmail extension or as the kludge of using a similar bot for this purpose. If such bots could run client side at our friends and if they only had access to the encrypted message body, it wouldn’t be that bad.
The event-countdown app is maybe slightly adjacent? Not really the same thing, if you want to be sent an e-mail at a specific time. Timezones would be a concern for a bot.
I agree that being able to auto-send prearranged messages to oneself or a group at a set time would be superior.