The reasoning behind a specific system may not be arbitrary, but why is one system better than another? People have also used 8 day systems, and 10 day systems. It would seem to me that biggest reason it is still in use today is “it’s the way we’ve always done it”. The inertia of the 7-day system makes change very hard, though there have been attempts over the last few centuries by both France and the Soviet Union. So, even if you could scientifically prove that some other system would be more productive, you would have a very hard time implementing it.

The idea that I will work a few percentage points more or less over my life, as a direct result of the phases of the moon, is, while perhaps technically correct, a fundamentally silly reason.