Short factual basis:
Because most manga/anime drawing styles do not allow for several characters' facial features to be actually all that distinctual, (
save for the artist/author applying scars, making one character always wear sunglasses, this bad guy has a fu manchu, and this good guy, seemingly, has whiskers?) the hair de facto becomes part of a characters' overall personality and makeup.
Maybe somewhere along the line anime/manga influenced real life and that's why you can partially explain the likes of
Shinjuku, or vice-versa, (art imitates life) but having some characters' wild-thing hairstyles makes them especially more recognizable as their entity, apart from the dozens of other characters that may be present within their own individual, storied universe. As to the outrageous hair colours present in anime, it's just taking the hair distinction to a further (perhaps more ridiculous) level of stating,
this person is wholly different from this other person. (e.g.
Character Ichigo has a name that literally means "strawberry" in Japanese, so, yes, indeed, it would make sense that his hair be "red/orange", given the name/hair distinction has already been set. Furthermore, regarding the Saiyan story line, the reason for the big hair is just as I stated previously, but when it grows longer or changes colour during certain battle scenes, this is just a quick visual indication to the readers that the relevant character has just amplified his/her powers by some upteenth degree, perhaps equals to how outrageous the hair follows his newfound strength?)
-- (
to note: This is semi-common knowledge to anyone who reads manga, and especially to anyone actually in-tune to Japanese culture, as the vestige of "flowing hair makes the (wo-/)man" is evident even in woodblock paintings from several centuries earlier. However, if you are a Western wonderer, this next few topics could help you more readily understand, if you didn't follow me above: Expressive Hair - Expository Hairstyle Change - Good Hair Evil Hair - Power Makes Your Hair Grow - Hair Colors. Although I am linking the trope-o-pedia, what I wrote above was just taken off the dome as an explanation as to why Anime more visually incorporates "the hair as the person" than anything really comprable to Western Animation/cartoons.)