Steve: before a few more aviation professionals respond in greater detail, I'll point out to you two general points:
1. Safety isn't a gimmick.
2. One of the insidious aspects of fatigue is that it slowly erodes your perception, and your ability to respond to cues.
At the end of a long flight, or a day of multiple sectors flown, the phase of flight that you are in (approach and landing) is where the need to be at your best.
If your "edge" has been dulled from fatigue (there have been studies a plenty over the years on that single topic) the risks in that critical phase increases.
Beyond that: the cargo in the aluminum tube behind you is people. It is not Game Boys, automobiles, wheat, coal, or other stuff as it is tends to be in a ship. (Cruise lines excepted).