Just to point out a few things....

Technically, the 'children' are, in a sense, a refelection of the
individual personalities we all have.  Believe it or not, the End of
Evangelion sort of made the point that we all want some sort of connection.
Even Asuka wanted a connection with her mother, not to be some kind of
'doll' as her mother kept referencing Asuka as.  If you watch the series as
a whole, one of the things that made Asuka the way she was, was to prove
she wasn't a doll, she was someone.  Unfortunately, Asuka also personifies
pride and egotism.

Consider this, we all show a bit of sadism when we prove we are 'better'
than someone else and we fall hard when we find out we are not the best.
Asuka actually portrays the extreme part of ourselves in this respect.

Rei is the rational and focused part of our lives to the extreme as well.
We try to detach ourselves from certain things, trying to be rational or
reasonable, and Rei is literally an epitome of just that.

Shinji shows the seeking of acception, of belonging.  One of the strongest
focus in the series was him wanting to be accepted by people and by his
father.  Another thing to also consider, is at the beginning of End of
Evangelion, Shinji does the one handed demon over Asuka, while near the end
he tries to strangle her in both his communion with Rei and at the end.
The thing is, Shinji is a person of conflicted emotions.  He does have
feelings for Asuka, as he also has feelings for Misato and Rei.  However,
in human emotions, all of us have the strongest emotions for those we have
the strongest feelings for, hence his centering around Asuka in that short
reality realization.  Also, remember, in the TV series mind-mess, again, it
was pictured of Asuka approaching Shinji to go to school, your typical love
interest type setting for the Japanese. (School Girl meeting Boy at his
house)

Another thing to consider is some of the other characters in the series.
Misato herself isn't a right cookie.  Even in the show, Misato admits she
does the things she does because she wanted a sense of connection.
Everything in the series was about connection between human beings and the
fact that people find connections by other means, even when some of those
means hurt.

What some people fail to understand about some of the characters, is that
the fact each person there wanted some sort of connection or intimacy of
some sort.  Look at how End of Evangelion ends.

The old man had an affection for Yui Ikari, he had it before and after she
got married to Gendo.
Ikari did this whole thing to see his wife again.
Maya, apparently, had a thing for Ritsuko.
The guy with the glasses had a thing for Misato
The other guy with the long hair, well... Dunno what he had in regards for
Rei.
Ritsuko apparently had a thing with Gendo, not to mention Ritsuko's mother.

Out of it all, it isn't the fact that Asuka didn't "add" anything...  Asuka
is another facet that we all have and the creator had to show it.  Shinji
didn't really have a sense of pride or egotism that Asuka had.  If you look
at him, he only 'felt' good because he got praised and he even said himself
he only piloted it because he wanted to feel needed.  Asuka piloted because
she wanted to be considered more than just a thing or a doll, and for a
person who has pride and ego, the last thing you want to be is considered a
thing.