Hmm, that's odd. I very recently had to cycle through using four different phones (one was dying, two ended up being defective, finally got a decent one), and each time I successfully transferred all my messages to the next. I thought that just transferred your messages though, not your keys (I could be wrong there).

But it is a bit silly that you need to manually move the file from the old phone/backup location to the new one without some in-app option to do so.