You are assuming that rider can output X watts continuously. This is not how humans work. Riders have different profiles in terms of torque vs rpm from their le

You are assuming that rider can output X watts continuously. This is not how humans work. Riders have different profiles in terms of torque vs rpm from their legs. A lighter bike means that a rider is outputing less torque, which he/she can sustain without downshifting to a lower gear, leading to overall increase in time not only during the climb, but also how much energy the rider has left in the tank after the climb for the rest of the course.