Shampoos are generally around pH 6.0, whereas soaps tend to the alkaline, over 8.0 (some traditional soaps can be pH 10). This means CP soaps are not pH balanced for our hair. After shampooing with products out of the right pH range, the cuticle of our hair doesn't lie down, and this can lead to abrasion between the hairs. This is a serious cause of mechanical hair damage, and once you have damage, it's hard to repair it, even with the most intense conditioners.
CP soaps aren't as soluble in hard water as most surfactants. Soap molecules in hard water are converted by double decomposition to form insoluble non-foaming salts like lime, calcium, or magnesium salts of fatty acids. This isn't a big deal on your skin, but it can lead to build up on your hair, leaving it looking dull and feeling kinda crunchy. They won't foam well if there are metal ions in your water - and most water contains metal ions - and they won't foam well in the presence of sebum. Given these properties, CP soap isn't going to remove all the stuff you've put on your hair and you won't get a feeling of being clean (or, ironically, your hair might feel too squeaky clean, which isn't a good thing).
Superfatting is the idea that you add more fatty acids than are needed (adding extra oils and butters), so you have free fatty acids in the soap after saponification. This enhances the lather profile, eliminates free alkali, and improves skin mildness. So you can superfat CP soap to get the pH down so it will be kinder to hair, but as I am not a soapmaker and only know what I read about it, please consult an expert soapmaker for more information on making a potential shampoo bar.
I know there's a recipe in this Voyageur recipe package for a shampoo bar (scroll almost to the end). I do have a sample of this product and it feels quite nice on my skin. I have seen people say they have used some kind of acidic hair rinse - apple cider vinegar, for example - after using CP soap and they like it.
Look for a series of posts on hair and hair care products in the very near future where I'll go into more detail about the biology and chemistry of our hair, so I'll get into more detail then!