The cover story of 'Only post-2I Children' is kind of needed, since Units-00, -01, and -02 are all set by the facts of Rei I, and Yui & Kyoko's Contact Experiments make it so that Rei, Shinji, and Asuka have to be the first 3 Pilots. Once you've gotten that far, you need an explanation as to 'Hey, why are all your Pilots 14 year old kids?'. Once you've done that, it's easier to keep rolling, especially as #1) 14 year olds are easier to manipulate and #2) if you're Gendo and SEELE, you know there aren't actually going to
be all that many Evas and Pilots. Even without the MP Dummy Plugs, they'd still have been able to fill out the numbers just from Class 2-A.
In any case, we know the entire Marduk Institute was a sham, and they weren't just picking the candidates out of a hat, but just as much they weren't making them all that high a priority. Despite Rei's injuries and Shinji's inexperience, they don't seem to have ever shown much urgency in looking for another Pilot or crash-completing another Eva in the early part of the series, when things were at their most thin in terms of combat ready Evas and Pilots.
We know (Doylist) that its a giant robot show convention that you can only have a tiny handful of said giant robots, no matter how critical they are to your planet's safety and how your entire civilization should be pumping out Evas, Pilots, and support units as fast as possible. If the Evas fail, everything else is moot. But in-universe, NERV, SEELE, and everyone display a bizarrely laid-back approach to things. Like others have said before, the Children should be living lives of private tutoring, constant training, and extensive psychological support, given how key they are to things. Instead, show conventions rule that they go to school like nothing is different, and treat 'being humanity's sole line of defense against the END OF EVERYTHING' like it's an annoying part-time job afterschool. Hell, 2/3 of NERV's Pilots live with a woman who managed to make a
penguin into an alcoholic!
Just repeat to yourself, 'Its Just A Show, I should Really Just Relax...'
That having been said, I've never seen a story where they try to use the elder Horaki sister as a Pilot, and only once where
Nozomi gets tapped.
Welcome to the new kids, and I'm sorry to say I'm going to be busy with a briefing in my day job until this evening, and then I'm promised to write a Panopticon snippet, but
then I'll be back to writing Asuka's birthday.