The main problem with that is that you can’t make the types very small with wood, and the singlemost expensive ingredient in this whole printing press concept is the paper.
So you would end up having books with very little text on each page, and especially in a slave economy, it would just be much cheaper to make handwritten copies, since you could cram a lot more words on each page.
And again, this is not adressing the issue of even having the skill to make paper in the first place.