That there's no offline vs mode is understandable within the context that the Japanese teams NEVER put local profile support in fighting game offline versus modes - not just Capcom, almost nobody. Namco, Arc System Works, whoever. Local versus just logs in P1, they even get achievements, and P2 is a guest / anonymous.
The only fighting game of the last few years that has profile support and even a proper multiplayer profile login screen is Third Strike Online, which was produced by a western designer. It's telling that only 3SO also has full replay recording for local, offline matches too. There's a big perceptual hole in the way Japanese teams approach these games.
The terribly inexcusable thing tho is that H&H is totally anti-social *online* as well, with no non-ranked player invites or battle rooms - THAT is a feature they already had code for, complete with spectator support now! The only reason I can imagine it's not there, is complete refusal by the designers (not suits) to see H&H as anything other than an online campaign mode where you fight randoms from the other faction for the global metagame.
I would be shocked if Seth Killian NEVER, ever, mentioned to anyone in the pipeline that players were going to want to play ability card matches with friends, and unranked, as well as official matches. If it never occurred to Seth either, holy crap, for shame on you Mr. Killian. Somebody in the chain of command should have known better than this.