If I go down to Figure 1. (the first graph), you see forward power vs. forward current. My main question here is: Why is the forward power at a given current greater for a smaller % duty cycle and less for a greater % duty cycle? If the power is on for less of the time, how could it be a greater dissipated power?
In short--because of math.
Ignore for a moment that it is a diode and just consider a resistor of say, 0.1 ohms with an average current of 10 A.
At DC, the average power in the resistor is the DC power, given by 0.1 x 10² = 10 W
At 50% duty cycle for the same average current the instantaneous current is 20 A (since 50% of 20 A is 10 A).
The average power is now 50% of 0.1 x 20² = 20 W.
Similarly, at 25% duty cycle the average power will be 25% of 0.1 x 40² = 40 W.
Diodes are non-linear, but the principle is the same. Power dissipated goes up as the duty cycle goes down if the average current remains unchanged.