I'm not really good at things like these. I don't really have an idea. It can't be that they are all artificial for several reasons, 1 they're not all artificial, 2 that would be boring. They're not all from just the games. They are all connected to at least one other thing in the list. I really don't know unites them. Hopefully its not something that after being told the answer I'll realise I knew it all along.
So, a month has passed, and we've got only two suggestions. Well, I expected something like that, we're not that active.
Anyway, I prepared an album full of images that show you what unites these characters and items, here. The "Shoulder Emblem" (肩のエンブレム,Kata no Enburemu)!
Although, that doesn't answer what they have in common.
My theory: all these things are artificial and sentient. You know, like artificial humans and not-quite-humans (Hello, Minerva). And we know that Archenemies have pseudo-identities, so they are sentient, as apparently are Legacy Weapons. Some of these things are obvious, and I'll try to explain the rest.
Black Beast: that image shows Beast made with Ragna's body, who is artificial.
Blood Scythe: apparently, its a really special weapon, but we don't know what it is yet. Maybe next media will tell us what this sword is, since it disappeared from the grave?
Hakumen and Susanoo: apparently, the Susanoo Unit is artificial, and it is kind of sentient, since it actually talked with Jin before he became its wielder.
Izayoi: not Tsubaki, but her armor. And if it is sentient, it might explain that Izayoi from the last cutscene of CF.
Mai Natsume: maybe that's because she's a Remix Heart/Grimoire/whatever.
Naoto Kurogane: that's a little weird, because he has a human body, but one of those marks is on his artificial arm. We need more info about what happened to him between BE and CF.
Nine the Phantom: uses a vessel made for her by Relius.
Spinner Superior: there's no explanation for this one. But since the rest fit in here so nicely, there may be a possibility that he's artificial, but there's nothing confirming it at this point.
My assumption is something around Terumi not taking everything with him when he left it, leaving behind the less desirable things. It'd explain why he has such different mannerisms as Susanoo, as with Jin as Hakumen. Of course that's just speculation.
Well, some part of Terumi being left in the Unit may be an explanation for that, and is actually the only explanation for Terumi's sudden personality change when he became Susanoo.
And there's a fact that supports your theory: even after Hakumen was "killed" with Hihiirokane, some part of him was still left in the Unit. Maybe it's actually impossible to completely leave it once one is recognized as Susanoo?
Yeah, those words are also said by Susanoo, though I guess in a different variation. Perhaps it was something he said at one point before rebelling. It's a bit vague on the circumstances, but Terumi it's safe to say he has been around for a long time. Though it's a bit uncertain on whether or not he was ever any different than he was now, I would assume he wasn't always spiteful towards Amaterasu. I really hope they end up explaining the circumstances behind it, to me it's probably one of the most intriguing mysteries of the series other than the creation of the Units in the first place.