You make me want to watch Evangelion. The explanation you give about Shinji reminds me of Kamille in Gundam Zeta.

I guess most protagonists/heroes in most anime who are male are either stable and strong (Amuro Ray to an extent or Duo Maxwell) or traumatised and driven to insanity to a degree (Kamille etcetera...). Oh well...

One of the franchises that inspired Evangelion was Mobile Suit Gundam, so it could be that some of that found its way into the show. Though, Ikari Shinji was made the way he was for two primary reasons. One, he was an analog for the show's creator, Hideaki Anno, who was depressed and faced a lot of hardship throughout the duration of the series. Two, Shinji was made in order to criticize the NEET culture that was prevalent amongst otaku at the time; in effect, Anno was yelling at anime fans for being unproductive and antisocial. Both of these elements are very, very easy to observe in Ikari Shinji. In a way, Shinji's characterization actually does a pretty good job highlighting some of the major themes of the anime. Unfortunately, the focus on character development and psychoanalysis actually ends up taking away from the plot to some degree, which ends up being a monster of the week show, on a superficial level. In the end, the fights with the Angels tend to be the least interesting aspect of Evangelion, while the characters and their mental and emotional issues end up being far more intriguing.