This doesn't make sense to me either. We still haven't seen them without their plugsuits on. I'm hoping this is a reveal in the next movie. After all the moaning and bitching about Misato strapping a bomb to Shinji's neck... Imagine Asuka telling Shinji that she woke up with a bomb collar too. "Stupid brat..."
But if it's not the case, there could be things to explain it, like you suggested.
I'd like that too. You did mention that drawing by Yamashita from 2010 that shows Mari and Asuka both wearing collars so it seems like they at least kicked the idea around at some stage of production. And Kaworu did say it was made for him (dubious as his narrative credit is) so it's not like it's something made just for Shinji in the context of the movie
That said, I have no real idea where NTE is going with this idea of cores not actually being CORES (as in a nucleus) but the WHOLE THING. It's rather needlessly confusing at the moment. (Doesn't really help that LCL is red now, introducing the possibility that "core" is nothing more than one possible solidified form that LCL can take...)
That could be possible. We don't see full-core entities pop up until late in the game, so I wonder... What if they're artificially engineered to be that way? Consider what we've seen:
1) The 12th Angel, which is made up of these peculiar hexagonal prisms that are made of core. It has an oddly manufactured look with all the pieces being so uniform like that (granted, so did the 7th Angel), and with Seele conducting experiments of that nature it doesn't seem outside the realm of possibility that they might have constructed or modified an Angel to fit their end game scenarios.
2) The Vessel of the Adams, which has been modified by Seele in some way. I think I pointed this out in my Eva Anatomy thread, but when it regenerates from Asuka's attack, it looks like a bunch of small cores mashed tightly together in a human shape. That could also just be an effect though.
3) The Mark.04s and their core blocks. They seem to be entirely artificial beings.
4) The Failures of Infinity, which were created as part of Third Impact.
This idea of a full-core being doesn't appear until 3.0. There was nothing like that in either of the two prior movies except maybe
the Giant Red Rei, so I wonder if it's not a result of Seele's meddling and research rather than a "natural" occurrence. All of those beings seem to link back to them in some way or other. I'll admit the 12th Angel feels like a dubious connection and I'm just spitballing that it might have been modified or manufactured.
So we have the following:
(A) Eva-01 is capable of being the Wunder's control system
(B) Eva-01 probably has an Adam's body, but surely not the original core
(C) Vessel might be an Adams' original core
(D) Vessel is "Wunder's original master"
(E) Vessel can take control of Wunder from Eva-01
So the Wunder might be keyed into the Adams' cores first and their bodies second? Maybe? Not sure I totally like this idea, but maybe it can spur on something better.
What if it works like an Evangelion? One of the Adams is a "designated pilot," so the others can
control it as we see with Unit 01 but this particular one has special priority status to override the others. Seele clearly had it there to counter the Wunder during their final play, I think, as there was nothing about the previous events that required the Vessel's unique skills and powers. But it also seems like the Vessel can only access the full extent of its powers under certain circumstances, because it only unleashes its true power after Unit 13 awakens and there was no reason for Seele not to take advantage of its superior firepower during the battle in Central Dogma to ensure their victory, or to bring down Wunder at any point before the battle started so it wouldn't even be a factor.
I expect the answer is actually pretty simple and hinges entirely on some unrevealed piece of information we couldn't possibly guess to tie it all together.
Someday I hope that we'll be reunited if that is what's destined to be. Perhaps we'll discover that elusive bible. And then we will finally be free!