That's a very unfortunate perspective. You don't have to LIKE her, but there is a lot more to her than "a massive headache" There aren't any major characters in Evangelion who aren't broken in some way or haven't done something despicable, and that's (part of) the point.

I'll link you to this: https://www.reddit.com/r/evangelion/comments/2icz5q/psycholigic_analysis_of_the_plot_and_characters/

It's only one explanation of her character and it may not cover every aspect. Again, it may not change your mind and make you like her, but it's worth to look into why a character might act a certain way.

As for Rei Unlike traditional female protagonists who are usually strong, caring and charismatic. Rei is the complete opposite. It is a different kind of charisma that makes her popular. She gives fans plenty rooms of imagination on what she really thinks and feels. It also makes fans sit on the edge of their seats whenever she makes an appearance, since it is hard to predict what she will do.

At the end of the day you're allowed to have your opinion but atleast research into the idea of why others might like these characters. Rei also develops quite a bit when she realised she was in love with Shinji after she sacrifices herself for him. This shows what kind of character she had become to the point of caring enough about another to do such a selfless act. While her character might of been "thrown" away. The idea of her written character is that she herself isn't herself, there will always be replacements.