The controller was an early phase trainee so it's hard to label it a systemic issue. "Workload" is a somewhat personal perception - he may have been preoccupied with thinking of other issues he perceived to be more important, got flustered & chose the easy solution of denying a clearance. Was there any indication to the controller that this course of action would be in any way dangerous? I very much doubt it. Trainees in any field often choose less than optimal solutions, provide a less than ideal service & just plain screw up, it's all part of the learning process. The instructor probably saw it as a minor inconvenience for the pilot that wasn't unsafe so didn't intervene - to be discussed later.
Why didn't the pilot simply deviate around the airspace? He'd deviate around weather so why is this any different? Or would that have presented a problem for this pilot as well?
P.S. it was "C" the pilot was denied the clearance for.