However, it is likely that you will never know about it, so don't worry about it. If the items are coming from free lenders, and you didn't intervene, it isn't costing you very much. It is hard to isolate this group and get an exact figure. You could gather the numbers, but it would involve a lot of time and paper tracking. In general, it is easy to see that it would be faster than a traditional request, as the request goes out immediately.
Most academic libraries have a liaison program with the librarians and each academic department.
Students are introduced to the idea during instruction sessions and at the reference desk. See your tech people for details. Ultimately, the only way to allay your fears is to try it. The good thing about Direct Request is that it is invisible to the user. You can turn on the option for a time and see how it works.