An absence of evidence is not evidence of absence. Yes, it is strange that there are no books in his will. However, this is not evidence for anything other than Shakespeare didn’t give away any books in his will. Using this to cast doubt on his authorship falls into the realm of conjecture.
Additionally, many prominent and educated Elizabethans made no mention of books in their last will and testament. Francis Bacon did not leave any books in his will, nor did Richard Hooker, one of the most educated theologians of the Elizabethan period. Reginald Scott, the author of The Discoverie of Witchcraft, also left any mention of books out of his will.