Not really, because in this particular sentence, "siz" is emphasized. If it was not used, it would emphasize the book or the verb. You use the subject when you mean "Why are YOU not writing that book?" Like "Why is it not YOU who writes the book?" Another example; Gördüm: I saw it. Ben gördüm: "It's ME who saw it!"
"Neden o kitabı siz yazmıyorsunuz?" Translation: Why are you not writing that book? Grammatically (plural)
"Neden o kitabı sen yazmıyorsun?" Translation: Why are you not writing that book? Grammatically (singular)
Correct other answer & not formal. Spoken one to one & personal.