Why do I want the model I use for coding to know Shakespeare or vice versa?

Because you communicate with it using natural language and real-world references and descriptions of what you want, you use emotion and emphasis (especially when re-prompting), you use examples and illustrative stories and common expressions. Understanding and interpreting all of that and replying in kind, to some degree, requires a large body of non-computation, cultural knowledge, or else the prompts are just meaningless words, and the replies will look like compiler output.