The causality can easily run in the other direction, with the desire to print things pushing people into using cheap, shoddy paper instead of quality vellum.
The cost of the hides and the labor of turning them into vellum dominated the labor of inscribing a page. Printing would not decrease the cost of finished pages, especially for small numbers of copies.
The decrease in the cost of paper resulted from the increased availability of linen rags, use of wind power in production of rag pulp, and the larger volumes of rag paper used for commercial records and correspondence before the invention of printing.
Your logic is that the drive to produce more books wouldn't lead to using cheaper paper... because paper was, at the beginning of the process, extremely expensive?
