The lack of (good) stories in fighting games is part of what turned me off the genre. Back in my single-digit years, I could play the likes of Mortal Kombat or Street Fighter, and not give a damn about why people were beating the crap out of each other. Nowadays, I do care. And what sucks more is that often, fighting games' stories are a case of exclusive pathways for the characters, and you won't find out what really happened until the next game. But unlike, say, the early Warcraft or Command and Conquer games (where there's only one of two canon paths), you have an entire roster to shift through.
I think the Mortal Kombat reboot (never played, but watched) had a pretty good idea, to make a flowing, single story, but even then, it's stymied by characters fighting at the drop of a hat, and the plot telling you how severe the fight was. Sometimes a character dies, sometimes it's just a little rumble. Injustice was a bit better (also watched, never played), but also suffered from the same problem. The only fighting game series I've ever truly gotten into was Soul Calibur, but by SCIV, I'd had enough. I'm not shifting through all these backstories in SC4 to find out what happened in SC3. SC3 did have a fairly strong core story (at least by the standards of its predecessors), but you still had to piece it together. If anything, the Soul Calibur adventure modes were more engrossing on a narrative level.
So, yeah. I think Netherealm has the right idea as to how to handle story in fighting games, but it shows how handicapped the genre is in making a compelling story.
Edit: Sonic Battle. Sonic Battle came out before the Mortal Kombat reboot, and used the same formula, of having one continuous story told over time from numerous character perspectives, and you get to build up Emerl along the way, from being absolutely useless, to the most powerful character in the game. And the story itself is pretty decent - not spectacular, but still decent, enough to make me care about Emerl's fate, and how it's a fate that he could basically never escape, and whatnot. I know, I know, it's a taboo to like Sonic nowadays, but, whatever, bite me.