I think your question represents a bit of a misunderstanding about black women and hair. I think the majority of black women don’t change their african american wigs styles because they want to “look white,” even black women who use perms. Black women do these things because their hair can be, Braids are simply convenient, as are perms. And why do black women dye their hair?
This question kind of assumes that black women dye their african american wigs “white” colors. Many black women might dye their hair red, brown, black, or even blue! Why do black women have to legitimize everything we do to our hair? We have to explain why we wear our hair natural. We have to explain why we wear our hair permed. We have to explain why we dye our hair or wear weave, whereas our white counterparts can do these things without an assumption that they are self-hating.
However, the answer to this question isn’t as simple as “because of the European standard of beauty.” I mean, yes, part of the reason african american wigs (notice I didn’t say “fake hair” – if you buy it, it’s yours) is because natural black hair is seen as inappropriate and socially unacceptable, but I think that’s only part of the larger story. Weaves do not have to be straight. In fact, I think you’re thinking of wigs, which are placed over the hair and are generally straight or curly.
Weaves are often sewn into braids to make the african american wigs, and I would argue that braids aren’t related to the European standard of beauty.but also partly because they think it looks nice. I suspect that this has its roots in Africa, though back then people may not have been using weave to style their hair in certain ways. Instead, their hair may have naturally been long enough to style that way.