I think the article would be better recieved if type 4 was called coily and type 5 was called crinkly for example.
It's ironic that in the real world you are most likely going to hear people refer to hair beyond type 3 as kinky or nappy. Those are real terms that real people use to describe the hair type... people don't use other terms as widely.
Yes they are real world terms but since I personally don't like it I choose not to agree with that term being used as the title of a category for black, or primarily black, hair. I know in the end it's just a word game and not really about the category itself but I am one of those who just doesn't feel comfortable calling herself nappy.