The first paragraph of your comment doesn't really connect with the next two. How does the pilot/psyche having to link with the robot/body implies Shinji, Asuka and Rei are part of the same psyche?

Anyway, you're ignoring all of the other mentally ill characters.

• Ryoji hates himself so much that he flirts with anything that moves just to try and prove to himself that he is worthy of love.
• Misato is so lonely that she's pushed into a toxic relationship with Ryoji. At her worst, she goes full pedophile just to get some affection.
• Gendo is so jealous of his own son that he literally tries to destroy the world so that he can be alone with his wife.
• Naoko was so obsessed with Gendo that she was not only glad when his wife died but also couldn't say no when asked to help him bring her back to life via cloning. She then killed the clone and probably herself.
• Ritsuko is fucking her mom's lover. Enough said.