The reason fatigue comes sooner for most people on climbs, despite power to the wheel being consistently a result of cadence x torque is because energy expended by itself does not equal torque. If a person expends more energy rocking back and forth, pushing the pedals at an ineffective angle, etc., while climbing, then less toque will be produced from the same amount of energy expended.

Another way of putting this is: if a power meter only measures torque and cadence, there are watts it is failing to measure. For most people, the watts spent NOT turning the cranks are higher while climbing than while pedaling efficiently on flats.