Except that quote is from the timeline where everything went according to her plans and the risks she took somewhat paid off;
With Q turning out the way it is, she has either massively miscalculated, or worse, fully intended both impacts and Shinji's role in them. As far as Rebuild!Yui is concerned, the former proves her happytalk wrong, the latter would be unforgiveable.
Yui's as bad, if not worse a monster than Gendo; She's just alligned with what we'd call "good" intended outcome wise, ie, SEELE's plan not going through and the protagonist living.
It's not like she saved Shinji's life out of the goodness of her heart back in 1.0; He's got her genes, and .spreading them around was something she did because she wanted to, to make her dreams of playing house come true.
She probably conceived him for the explicit purpose of doing this to him, or at least, planned it for a long time. She might've used her inbuilt baby factory and not a lab to make him, but basically, Shinji is to Yui what Kaworu is to Keel and what Rei is to Gendo.
Gendo especially Rebuild!Gendo did more actual raising than her, and he justified his absence with exactly the same "well, I'm working on making a better worl here!".
At least he admits he screwed up and shows some regret.
That is not to say that Yui's words, especially in the context of the original series, are to be thrown away - a character can be right about some things and wrong about others, making one character only sprout things you find "right" or "wrong" makes for boring villains and preachy heroes.
I think that what the previous poster wanted to propose with that "Shinji dies happily with Yui's bessing" scenario is an ending where his parents stop messing with him, so to speak, or no longer expect him to fight their battles for them - "Allright, you've done reanonably well in that unreasonable thing we asked of you, so relax now. Do what you want."
I can see the justice/ justifying closure in that, even if not all such scenarios necessarily require Shinji's death.
As for actual death predictions. Gendo amassed too much bad Karma and Fuyu is old. Rei always dies, I've given up hope here.
Misato is trickier; There's 'mentor occupassional hazard' on the one hand and the stereotypical ending for a character who's mad with revenge on the other, but no reason she can't live and... make an epic hopeful speech to the survivors at the end. 50/50.
Same for Shinji - It feels like killing him off wouldn't be Anno's style, but the kid got too much bad karma, be it unintentionally, and little chances of a future.
Misato could just shoot him right after they defeat NERV, ala "Now you're the only one left."
Personally, I'd take a well-written tragic death over an ending where he lives, but is likely to be gunned down in the matter of a week due to human nature, or, at least, doesn't seem better off for it.
Although I'd obviously prefer it if he finds some place for himself in the world.
Asuka is less likely to be killed, but I wouldn't put it past Anno.
Sakura, Midori and Hideki need to survive to rebuild society. If they kill Sakura, I'm seriously ragequitting.