This is an interesting question. I can imagine the technique being useful for acquiring the general skill of language learning, but a language itself I can only really see the “what” and “how” books being useful, not the why.
Nor can I imagine this technique being very helpful to learn how to ride a bike, although I imagine it could be useful to become a competitive bike racer.
The distinction between skill and knowledge seems a good start, but it seems like there’s more going on here.
Maybe the “why” book for a language would be something like reading manga for someone wanting to learn Japanese—something that makes the language and culture seem cool and something that you want to learn. :)
Given that learning a language also includes a fair chunk of learning the culture (e.g. knowing which forms of address are appropriate at which times), reading literature from that culture is probably actually useful for accomplishing the “Why” book’s goal of explaining the mindset and intuitions behind the skill.