Reflecting upon a couple of recent games I've played, I need to start paying more attention to how game designers manage to use battles as a mechanic for character- and world-building.
Undertale and Everhood both use battle themes and battle mechanics to help build character for their small casts. A memorable battle theme makes for a memorable battle after all, and because these games have interactive battles they're able to add unique or thematic components to battles that are in-line with their characters.
After the baseline mechanics are established, the designers can make interactions feel unique by tossing in changes to the formula. A character can be made to seem intense or goofy or strong or mysterious by having non-standard moves or gimmicks in-line with this personality trait.
I also saw in Live A Live how battle systems could be used to tell stories and world-build. By changing the formula just a bit, like giving your opponent the experience points when they're your disciple, the game subverts expectations in noticeable ways that build upon the game world.
This obviously comes at a cost -- per-enemy soundtracks or coding in completely different ways for a battle to behave are costly compared to just adding more dialogue, but I feel like a short game filled with unique content that uses it's own mechanics to tell stories is always going to be more interesting than a long game that just re-uses mechanics.
I'm sure everything in this post has been said a thousand times before. However, I'm really enjoying finding these things out for myself and learning new things as I play through my library.