Ultimately, when people think Soul Calibur, they think single player. I still hear callbacks for SC2 Weapon Master mode to this day. I am reminded of an interview with Harada, where he mentioned that tournament players only make up 10% or so of a game's userbase (don't quote me on this).
SCIV and SCV single player have been abysmal, and I think this is the main reason why SC does not have a "big name" today. SCIII's single player was great (in my eyes), but it was PS2 exclusive, so I don't know how that affected the general populace. (Never mind the glitches, but honestly, for casuals the only glitch they would know about would be the whole "vanishing save data" bit.)
If the shareholders do not push NBGI/Project Soul and they are allowed to create a good single player along with the core experience, I think things will do well. I personally believe having a "draw" to the series like said single player will result in higher tournament turnout (or at least some passing interest) since SC does not have "brand power" like "I remember playing that at the movie theater" Street Fighter. Of course, online play is another "draw" that should be focused on (if they have any magic tricks for that, here's hoping...)
As for what I would want myself... I am pleased with the direction the series is going, and I don't have any strong opinion on the matter (I think whatever they do next, I will readily play without hesitation).
If I could request anything, though, it would be... more violent animations. Like Sophitia's toe stabs, Nightmare's SCIV A+K, Zasalamel's right-side throw. Not necessarily unrealistic, but still over-the-top, creative in a sort of twisted way, the kind of thing that would make you stop and stare, if you were passing a storefront monitor on the sidewalk.
Maybe "violent" is too strong of a word; I mean heavy in intensity, passion, etc. There is a difference between violence and gore; I find modern developers can be heavy on the gore, but the actual content is not very violent at all, but rather detached.
I know when I saw FilthieRich demo this on the Gamespot stream, SCV was as good as bought for me.
(As a small sidenote, I think a beginner's character, whose "damage" attacks (i.e. 3B and the like) lead to attack throws on normal hit instead of combos, would be interesting, too.)