I think all of this comes down to context. In RE you are generally very alone and in the dark so finding the torn pages of a diary makes sense. On top of that the key plot details are never in there and it is about flavor text or expanding on the story. They are nice but you don't need to read them to understand what is going on. To write characters that explain these things would feel more contrived than the setting would lend itself to.

FFXIII on the other hand is just bad writing. So much stuff is tucked away instead of having one of the many characters explain what is going on. This is suppose to be an epic RPG quest and instead of towns with NPCs that you interact with a mysterious data log gets filled up with information that you don't ever gather on your own. You never run across a library and gain entries for the History of Cocoon. The game just up and decides, this is now kind of maybe relevant.

Xenosaga III on the other hand is a bit dicey. The datalog is nice because this is the 3rd entry in a series that has a building story so being able to get filled in on character motivations that have been previous established is nice without having the bog down the narrative and revisit/redo all of what took two games to accomplish. On the other hand there is plenty of stuff in there that isn't just backstory and the game thus far. In a perfect world, they would have been able to tell the story through more locations and characters and everything that is established but they were clearly running out of money.

I think this is more along the right track for a datalog. Backstory/Character stuff from previous entries and entries for books and notes that you find. Those books and notes could be a diary or explaining how to dismantle and assemble a Glock 17...but you should have to find these.