I tried to pick ratios that wouldn't cause riots in the streets, haha. Interestingly, 7-3 is still less work overall than the current standard 5-2. I could get behind a 3-1-4-2 system.

I used to have a rolling 4 ten week, so Monday off one week then Tuesday the following etc. The best part was the week you have Friday the next you have Monday so it's a 4 day weekend every month. But the job was so fucking boring and they'd still come around every day 9 hours into the shift asking if you wanted to do 2 hours overtime... So 4 days was basically work, go home, shower, eat, sleep repeat. I personally need some wind down time each day but I can definitely see how some people would like this setup

I had the option for 4x10 and turned that down. I'm barely useful after 8 hours. I can't imagine 2 extra hours a day.

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.