You'd still need to figure out what was a relevant piece of information to include from the log though.
On a related note, something I could see a use for would be a "battle report" type of thing. Going down the narrative route should be easier (and would be kind of cool), but it would also grant a better insight into the AI's decision making process (at least if implemented well) no matter how it was done. Not only would it help newcomers understand how to script for battles, but I'm sure even veterans would be interested to know precisely why their water mage decided to spend all of his crystals on summoning elementals when the enemy began to rout