The problem isn't the fact that anime has crazy hair colors, it's that it has crazy hair colors in this setting. I'm not going to complain about Magic Knight Rayearth having characters like it does. I know the difference between fact and fiction; do you know the difference between authentic and inauthentic fiction?
I don't really like the argument, but I see what you mean. I thought the same; she was designed in a way for the sake of being the peacock of the bunch, essentially.
It's worth noting that the orange-color is probably the most popular highlight/dye in hair color in East Asia, which helps it along. Purple, red, blue, etc highlights exist, but are incredibly rare, let alone an entire head full of that color. Last time I remember seeing blue hair was someone doing that for a concert, and that was a wig...it takes an absurd amount of time to dress up for that sort of thing, so it's not something you'd see at school every day.
It just doesn't match with the idea that these are supposed to be normal people doing mundane, everyday things, unless you have a character who has a trait of being purposefully outlandish (See: Luna Lovegood from Harry Potter for example).
The funny thing is, these hair colors would feel out of place even if this was all taking place in an American school...it fits even less in a Japanese school. God forbid if Singapore ever gets a animation industry, that would be even more laughable. Even the kids doing something as simple as bleaching their hair around Asian countries are associated with rebellion...taken to its extreme, it's stereotyped to being kids that tend to ditch school or join gangs and the like (Gyaru culture, for instance). Yet, the characters portrayed in these stories tend to be pretty mild-mannered, good kids. Actually, GTO nails what you might see at a typical East Asian school pretty well.
So you see, it's not the outlandish hair colors that annoy me...it's the setting it takes place in and the way it's handled.