I see chat bots as a new UX channel that complements the other existing ones: Mobile apps, desktop apps, tablet apps, wearable apps, VR apps. Chat bots will be primarily used for use cases where the user has already initiated a transaction, and wants to continue communicating around that transaction.
The transactions might be about traveling, going to the movies, ordering pizza and so on. They will be things that are small enough to not justify the distraction of sending a push message and launching the dedicated app. Just small notifications that you can open in the chat application that you are already using anyway.
Facebook Messenger will have a clear advantage in this, because people already use Facebook to sign in into desktop and mobile apps. Once you're signed in, the chat bot can send you notifications because it knows your Facebook ID. This will not be as easy on most other chat platforms, which will require somehow connecting them to the customer first.
Interestingly, wearable apps and chat bot apps seem to have very similar use cases. Smartwatches were intended to become a lightweight notification platform always present on your wrist. But the use cases were so modest that they didn't really warrant buying 300€ watches – that would have required a real killer app. Chat applications, on the other hand, are already omnipresent everywhere and can easily be extended for transactional notifications. The only big risk is alienating users with unsolicited spam messages.