I tried this, years ago, since I have natural ( a.k.a. afro, no relaxer ) African American hair. It did not agree with me. Some swear by it and I have seen beautiful hair that thrives on it. I just do better with shampooing regularly. I do however "co-wash" daily when I choose to wear my hair in its naturally coily state ( instead of a blowdry + flat iron or wet set ), but I still shampoo every four days to start with a fresh canvas. My hair styles better and my scalp is happier when I shampoo every few days.
On a side note I am on a hair forum where someone is experimenting with using only rosewater, apple cider vinegar, aloe vera, and her natural hair oil ( sebum ) only. It is very interesting and I see how it works in theory. Her hair looks good but I am just not sure I could get into getting use to the smell ( which she says is just "earthy" once you adjust to it ) and the fact that you have to go pretty basic as far as styles are concerned. She lets the oil build up for awhile and brushes it down the length of her hair. She only washes with the apple cider vinegar, moisturizes with the rosewater, and styles with the aloe vera. Refreshingly simple. I am not that simple, but maybe someone else could benefit from her approach.