Evangelion is not so secretly Anno's very own form of therapy for himself. While End of Evangelion was bleak as hell, Shinji's lowest point (so far anyway. Rebuild had him sort of, kind of, cause another apocalypse and almost cause a third?), the kid ultimately did choose to reject instrumentality even though he briefly gave in completely.
Rebuild having a more fulfilling ending is mostly Anno being in a mentally healthier place than anything.
Emotion and expressing it is a healthy thing. Anything in excess can be construed as "bad," especially if it ends up just becoming self-pity without looking for recourse to grow (easier to forgive in children, more egregious to see in adults that should have hopefully grown into better, still context dependent), but the sheer magnitude of the issues characters people tend to label as "crybabies" are far beyond what most anyone can realistically claim to ever need to deal with. A real person would fold confronted by the weight of the fiction someone like Shinji encounters at half the age where the brain is expected to reach something even approaching full maturity.
What examples are you thinking to be excessive based on the context? What's 42% of the pain of having a spear go through your skull translate to where, up to that point in life, you were just an emotionally abused child with abandonment issues? Or taking on a responsibility you have no business being given and being guilted into it by the adults in the room? The ultimatum was fight the Kaiju seeking to kill everyone with no training, or let this injured stranger child you just met do it and die trying, all because no one older is capable of doing the job you shouldn't have and there's no guarantee you can do it despite being the only and last hope? I'm not even talking about the escalation later, just the first episode.
