Um, Eternal Sonata sorta does....
At least, in terms of the Momento time loop-de-doop
You save your daughter from her captor.... but not her disease, and not mankind's eventual demise....whomp whomp
Tales of Eternia you save TWO
Plural'd the threat there.
Radiant Historia you temporarily save the shitty continent you're on.
...I don't think they actually "fixed" the problem beyond the "warring nations" A-plot though.
Breath of Fire III
You spare...your race? And tell god to fuck herself so you can have nice things.
I"m going on a limb with Drakengard... but you spare your mind because how shit gradually turns to shit, and shitter, and shittiest.
My examples suck ass.
Baten Kaitos you save crops of continents that float in the sky and not a world.
..Hmm, Wiseman wanted to change everyone into a Magic deck.
Final Fantasy VII technically because
naw, I'm fucking with you, it's "save the world" 1000% because Sephiroth is a dick-mobile