@Robby:
I haven't watched original Gundam in over 20 years and only once so I've certainly forgotten details. I remember a couple of times where he was exhausted and didn't want/couldn't fight anymore just due to pure tiredness. The only time I remember him leaving was when his commanders were chewing him out and saying he wasn't even a soldier and shouldn't be there in the first place. And then he took the Gundam with him.
If you're thinking of something else I'll have to take your word on it, I don't remember much beyond the big iconic stuff that made it into the musou games.
I actually looked it up because I wasn't remember too much either but Shinji didn't want to pilot the Eva because he was insecure I'm pretty sure. Not because he didn't want to kill people. Amuro refuses to pilot the Gundam because he was exhausted, yeah, which is an actual consequence of a child piloting a robot. Shinji being insecure doesn't have anything to do with "the real life consequences of a child piloting a robot" though from what I can see. Asuka is more like a typical mecha protag for most of the series and doesn't have any problems with it until she starts getting insecure of Shinji later in the series. Most of Eva actually seems to me to be focused on the psychological issues of the main characters, which exist outside of the robots and fighting. You could say that you have to have psychological issues to be a pilot, though Toji didn't. Your mom being dead doesn't mean you have to be psychological broken, and the mom's spirit being in the Eva is as far as we know the only requirement to piloting the Eva (though there is a vague selection process). They're sticking mentally ill people into stressful situations and then going "look at how broken these people are", and I don't see how that has anything to do with deconstructing mecha anime or showing the consequences of kids piloting robots since like I said these issues exist outside of the robots even if they're exacerbated by them (though actually Shinji's self esteem increases since he has something to be proud of himself for even if this doesn't hold the entire series).