Does it matter? Fix the broken process and you get happier developers and better productivity.
Consider it in different words. "Tired people are bad for themselves, for process, and for projects." To many, this will read as "hire folks that aren't tired." Worse, it will be "your folks are tired, so they will make things bad for themselves, their processes, and their projects."
At best, you will get people who will see it and victim blame in a way that won't help. "You are jeopardizing our ability to succeed with your tiredness. In addition to your current tasks, I'm assigning you the job of getting less tired." So... odds of increasing wakefulness, slim.
Now, it could turn out that it is something you can fix in this way. I don't know and that is my point.