If your messaging system goes down, that's a bad time to learn your team became reliant on that messaging system and is now unable to coordinate to fix it. Same reason system status pages shouldn't be hosted on the systems they support, so you don't lose them when you need them most.
Alternatively, it makes outages that much more painful. Also, for stuff like "external mails go to the other folder", usability issues wouldn't go unnoticed.
