The pressure, if any, would likely not come from Academic Departments. I can see how the admin side of the institution might want, for financial reason, to encourage purchases through the bookstore... Also, in order to have books available for first day of classes, it is difficult to do anything other than ordering through the bookstore.

At one of the institutions I've worked as a senior administrator, we did contemplate no longer having a bookstore and instead relying on Amazon/Chapters given their excellent service and general book availability. However, I would never have supported the idea of contracting out to some firm that dealt with a limited number of publishers.