The fighter who I'd most like to see here, and I think is most fitting(read as would be well received) is Heihachi. But given mii theory(which is a prevalent as ever after Geno) it seems for whatever reason he was passed on. Next in line would be Sub-Zero or Scorpion(maybe even before Heihachi), but they're likely off the table due to the series being heavily restricted in Japan. A whole bunch of sword fighters from Soul Calibur and Guilty Gear, now I feel would also be poorly received because we just had a sword character. As far as impressive fighters go it really only leaves Chun-Li left. There is also Akuma, but we'd be pitting legacy against cool at that point.
I don't know, I can't talk a lot about Soul Calibur but I doubt Nightmare (or anyone else) would be just a "sword character". I think you're missing the fact that we're talking about FGC characters with swords, so they're not going to use their swords in the same way Marth or Shulk do, for example.
Also not the first time I say this but I wouldn't really count Sol as a sword character. I guess the Junkyard Dog MK II (cool name huh) kinda looks like a sword but it has a pretty unique design, so it's not the traditional sword you see in Smash. Also, because Sol uses it in a very distinctive way. Plus of course he doesn't use it for every move or ability he has.
I think checking this list of his moveset in Guilty Gear Xrd (it has pictures) would prove my point:
dustloop.com
About being poor received because they use sword-like weapons, I mean... people will always find a complain. At this point I can't take seriously anyone who complains about swordfighters.
Besides all that, I think you're forgetting the fact a good chunk of people will probably complain if they add a FGC character. It happened with Terry and it will happen again, regardless of Nintendo choosing Chun-Li or Nightmare/Sol Badguy. Maybe it's just me but a significant portion of the community doesn't seem to be very welcoming towards the idea of more FGC characters, at least until they're able to play as the character.
OK is there actually a chair, or did people just photoshop it in because they though it was funny?
It's a random PC mod that became sort of a meme in the DMC community recently. The chair isn't really there in the game.