Brawl's premise is built on the almost same exact narrative as the other games you know. It never bothered doing anything with that narrative as that plot was completely out of the left field and based on something entirely different. In a sense I always found that the appeal of Smash Bros.; especially the metaphors one can draw with the original game.
Fair enough. I haven't played Injustice so who knows, maybe it's the best thing in crossovers since peanut butter jelly. I can see why the removal of SSE-like cutscenes might be a bother but I can also see why, if from a developer perspective, Sakurai wanted to avoid doing another SSE.
Unless I'm mistaken, Sakurai himself took the creative duties of Kid Icarus Uprising simply because he wasn't satisfied with how SSE turned out in the long run - which is why I don't get the arguments against him that he's somehow ass-backwards. The guy can easily do a good single player campaign if he puts his mind to it but I think that in terms of the general picture here, he'd rather give the crossover spice through things like event modes, character trailers and a regular old adventure mode, and that's completely fine in my eyes. Though that's just me speaking.