YUI:“I'm also considering a domestic life.
Of course, that's only if I can find someone nice.”
UrsusArctos: (Due to formatting issues I moved a rather substantial discussion on Yui's character and motives into the "additional comments" section).
Additional Commentary
Dr. Nick: We're given important glimpses of her backstory, but Yui still remains mysterious to this day. The potentially extracanonical revelation that she's the daughter of an influential member of Seele feels like an important puzzle piece that should've been in the show proper, as it explains how this random young scientist knows about the conspiracy she then sets out to thwart.
But when we start considering the details of her plan, things get highly speculative. For example, does Yui choose to let herself become Unit-01's resident soul and then manipulate the proceedings during 3I to her liking simply because it's the only option, and stopping Seele outright is impossible even for her? Is her becoming a living monument to humanity's existence just her making the best out of an unfortunate situation, a consolation prize of sorts ("I will go along with the flow of things.")? Because if she prioritized the monument thing over shutting the Third Impact down cold, that is morally suspect. It's no wonder that "Yui is a stealth villain" is a pretty popular fan theory.
Similarly, consider the cold pragmatist/sociopath reading of this line: is Yui implying "I need to have a child (who'll become an Eva pilot I can manipulate) for my plan to work"? Seele doesn't yet have a practical roadmap to their end goal, but is Yui, being a scientist, ahead of the old religious weirdos? Has she already foreseen pilotable biomechs at this point in time?
UrsusArctos: Yes, it's for good reason that "Yui is a high-functioning sociopath" theory has gone everywhere from heated EGF discussions to Shinji and Warhammer 40K where Bhepin turned it into dramedy in his usual absurdly over-the-top style. A lot of Yui's actions, such as "showing Shinji the bright future" while disappearing inside Eva-01 and traumatizing the poor kid (and turning her husband into an obsessive wreck) really come off as the work of a sociopath, especially since we don't have any information about why she thinks doing what she did was a remotely good idea. Even talking to the single, lonely Fuyutsuki about marrying the right person could be interpreted as a callous attempt at manipulating Fuyutsuki's feelings. Given just how much of an upward battle women have against sexism, especially in Japan, I really don't see someone in Yui's position willingly giving up a promising research career for cozy domesticity - it's so blood-boilingly anti-feminist and misogynist that it invites suspicion on the woman voicing such an opinion.
On the balance, I'd say Yui benefits from a lack of backstory in exactly the same way as Seele. By being a cipher it really is hard to pin down her motivations, good or bad, and it leaves it to the viewer to try to piece something together from the scraps that we are given, utterly unlike the deep dives we get with Shinji, Misato, Asuka and Rei.
