In these situations the savings may not be obvious and may not sit inside your part of the organisation. In my business, any kickbacks go into a corporate travel centre and my business - separate p&l - doesn't see them. We just see standard fares and a booking fee.
I usually go with that, but it would irritate me if I had a constrained budget, and certainly if I was in a university with costs coming from funding. In that case I'd request the central savings be added to my budget or book direct.
there are some employee tracking functions of TA bookings, where I go direct I have to manually update an iSOS trip record.