I don't train LLMs myself, but my impression is that general knowledge has lead to more intelligent behavior on specific tasks. The voluminous training set is imporant.

But even besides that... Yesterday I prompted a feature by referencing a specific Monty Python skit. Does the coding tool need to know Monty Python? Maybe I could describe the feature in other terms, but it sure was convenient to have this shared knowledge. I don't see why Shakespeare would be any different.