That's obviously the short version and it is a complex compared to standard DC motors, but brushless motors are more efficient and that's the benefit. Better efficiency means you get more mechanical energy per unit of power, which is a good thing! The bad thing is, hall-effect sensors are relatively unreliable in the hot, high voltage, rock-and-roll insides of electric bike hub motors.
In my case, the villain was voltage. Although, I certainly didn't help the situation when I crashed the stupid thing.
When the bike fell, the sensor and power leads--8 wires altogether--were crushed and severed as the axle ground against the concrete. As a result, the current intended for the motor found its way to one of the sensors and killed it as the heat changed the internal composition from silcon to silcon dioxide. The controller, as I said before, depends on these sensors to distribute power, so the whole system fails with the loss of even one of them.
Efficient, yes. Robust, no.
Sure enough, after repairing the wiring, I found that the motor didn't turn smoothly anymore. Rotation was jerky and it didn't produce much torque. This is known as "sputtering." There were also dead spots, where, if at rest, the wheel could not begin to spin. Major major problems. After a little research and hanging around the Golden Motor owner's forum, I learned that my problem was a failed sensor and it needed to be replaced.
This Instructable documents the process I followed to replace this sensor and bring my bike back to life.
First, a thousand thank-you's go out to myelectricbike, who walked me through this step-by-step, provided much of the information you'll read here, and is singlehandedly forging a first-rate forum for Golden Motor product owners.