A Tower Controller reported a Flight School took an unreasonable amount of time to respond to an aircraft which got a flat tire when landing and became disabled on the runway.

Narrative

Aircraft X got a flat left main and were unable to exit Runway XXR. Controller In Charge called Airport Operations to have an escort meet a tug at Taxiway X. Another controller; not on position and in the process of going home; called the university to have a tug meet the escort at Taxiway X. Airport Operations responded almost immediately. Airport Vehicle was waiting at Taxiway X impressively quick. Controller In Charge called university Airport Operations again after approximately 10 minutes and no sign of a tug. Our primary runway was unavailable and the response time by university was horrendous. Arrival was notified that all aircraft would be circling to Runway XXL. Constant IFR inbounds combined with patterns and stages created excessive workload for the Local Control Controller and single runway operations.University seems to be unaware of the impact a flat tire has. Whether it is on a runway or blocking an exit from a runway; it is increased workload on all controllers. It is common for University to drag their feet in response to a flat tire. Also; it is common for University to show up unprepared to fix the flat and have to go back to the ramp to get parts. University response time needs to improve. The University maintenance van should have a main gear for an Aircraft Y and a main gear for an Aircraft Z in it at all times.