Joining on the conversation about Shinji, I agree that he is a good character even if he isn't someone you'd want to be. This goes back to the previous discussion about whether all anime is supposed to be entertainment/fun (regardless of the discussion of what the meaning of entertainment is), and how it obviously doesn't have to.
Not all fiction has to be wish fulfillment, not all characters are meant to be awesome guys you'd want to hang out with. Welcome to the NHK's MC is another example of a character that isn't "fun" at all, because what I got from the show was that it didn't just want to entertain the audience as much as it wanted to show us the life and struggles of a stylized and somewhat caricaturized version of a hikkikomori.
Shinji's similar in that Eva isn't a show meant to have you praise the giant robot and their pilots as they obliterate wave after wave of bizarre angels. It was a deconstruction of the genre, which meant exploring a harsher vision of the generic humungous mecha shows. The mechas weren't just awesome gadgets, the team was made up of flawed humans which all had their own issues that they struggled to sort out, and the MC had no backbone because he was constantly being treated that way (either by being ignored by his father, talked down to by Asuka or pampered like a little boy by Misato).
The EVA pilot crew had among its ranks a girl who began belittling others weaker than her as a way to cope with how her mother commited suicide alongside a doll believing that it was her daughter, another girl who realized that her actual self was interchangeable and that each of her clones weren't worth a damn, on top of merely being a tool created with the sole purpose of fulfilling Gendo's wishes; and then there's Shinji, who only got called as an EVA pilot candidate because he was the most likely to synchronize with EVA-01, which had his own mother as part of it. Shinji keeps trying his best to appeal to his dad, but all Gendo has in sight is being able to recover his lost love, and doesn't give a damn about using NERV, his own son and countless clones of his dead wife to achieve his goal. Shinji also gets to experience how everybody else around him starts showing their true selves through cracks in their façades and eventually break down in horrible ways, which would certainly end up affecting someone with low self-esteem in disastrous ways.
Honestly, I liked Eva's message in the later episodes about how everybody wears a mask and how neither what we see in ourselves and how others see us is a complete image, as the mental picture of who we are is based on perception which is fundamentally flawed. It also managed to avoid the cop-out of "why don't they just talk their problems out?", since many of the flaws characters had were quite complicated, meaning that they couldn't just open up to their friends and colleagues (remember that none of them had close family at all... Shinji had Gendo, but he was an absent father the whole time).
ance All Night*.
