In regards to the Story mode, while I'm almost sure they'd probably never take things to how I imagine a dope story mode could go in fighters, I have a few thoughts on how they could embody some new elements to their story mode (and probably other fighting games in general).
For one, if they're truly serious about the mode being a lot more important this time around, perhaps they should release the story in episodic content form whenever they have new character packs come in. Not as just an aside, but have the story truly progress within each update. This isn't to say that the initial roster's stories have to be on cliffhangers or anything like that, just that newer facets of the story and character would come to play as new/old characters come in DLC and have have an actual effect on the previous characters stories as well.
The other, which I feel would be an even more evolutionary form of handling story mode in fighters (and as such, probably even less likely to happen) would be that your story mode would actually have the option of fighting other online players whom are using characters that pertain to your fighter's story rather than just the AI. This could be done on the low level of importance sides of your fighter's quest like just fighting your average jobbers and the more significant fights like mid-stage bosses/bosses/rivalries, etc. I imagine it would mostly be at random, though, they could still tell brief story elements even for non-major fighter interactions pre-fight, which could also double as the load screens/wait for finding online opponents that are using said other characters. It'd be even iller to have this include their rank system for finding equally skilled, lesser skilled and more skilled opponents to be your story mode opposition, as that could be a bit like a difficulty setting for the story mode itself. It could even move the story forward still if you lose and have the story incorporate the win or loss to those specific characters as well, rather than the obligatory fight quote screen only. I figure this would be an efficient way of having online only gamers that normally wouldn't even bother with the story mode more of an incentive to play it, as it'd be suiting the best of both worlds. Obviously, it can be selected off if you'd opt not to fight anyone online with your story mode.