My big annoyance with second season Shana was the way that the title character was deemphasised in favour of Yuji, who was the centre of everything and got a series of power boosts. The third season seems to have been written in order to push my buttons.While it technically hasn't ended yet, watching the final season of Shana has ended up mostly being an intellectual exercise in realizing how detached I am from the story and characters after all this time. It's not badly done by any means, it's just something that I would have enjoyed far more three years ago. For whatever reason though I just keep watching and snickering about how much I apparently have come to dislike Yoshida and her entire archtype (That is, the childhood friend or otherwise "normal" love interest who has no powers or cool abilities or ever does anything slightly useful or interesting and has no chance in hell of winning over the main character from his primary Alien/Robot/Witch/Catgirl/Detective love interest but will whine about it constantly until the end of the series.) It does have some fantastic names, though. The series has got to be the best random badass title generator of all time.
Regarding normal girls, I can think of at least one show where the normal girl beat the apparently primary love interest, aided by the fact that the apparently primary love interest (who wasn't the psychic alien AI) was crazy. That was about 15 years ago, mind you.