One of the reasons you don't want a real chat app to be implemented like this is that KBFS has to be pretty conservative about conflict resolution. If you and I both edit `foo.txt` at the same time, then we're going to wind up with something like `foo.txt` and `foo.txt_CONFLICTING_COPY_2020_02_14`. (Basically the same as what Dropbox does.) But of course, that's not what we want to happen if you and I send a message to each other at the same time. There, we want the server to just tell us which one came first, and that's fine. There's no real conflict. (For larger gaps, where my phone has observed your message before I send mine, Keybase will indeed sign over that observed history, and the server won't be able to reorder the messages.)
If I send you a message for the first time, your FS (nodes connected together) gets a request/ invitation to mount a new FS/folder containing files where each is a message. Want to add someone? Invite to mount the collective FS. Instantly the new member can see the chat history and begin writing new files/messages to the FS.
They don't do the messaging threw the file system, but I would argue that's an implementation detail.