I am familiar with the argument you are making, but I haven't seen that in practice. I noticed that if you give someone an extra day off or extra 3 days off, less work gets done rather than more.
Here in Hong Kong we have quite a few 3-day or 4-day working weeks (due to public holidays) and I have never once seen more work being done on those weeks.
I don't think doing it as a one-off counts. I think the argument is that an extended time on 4-day weeks would in the long term allow people to settle into a more well-rested rhythm.
I work sometimes a 4-day week because of Sweden's regulations after I have an on-call week. It happens quite often, every 3-4 weeks depending on our rotation and I can say that having a steady 4-day week makes me and most of my colleagues more productive.
So I have seen it in practice, as a counterpoint to your anecdote with another anecdote.
That's different. When you do a four day week it should be same hours, eg 40 hour week is 5 X 8 hour days or 4 X 10 hour days. Giving people a holiday and then expecting them to make that time up during the rest of the week is ridiculous.
No, that's not normally what a four day week means. It generally means less hours, but you also wouldn't normally expect moretotal stuff to get done, but you might expect a similar amount to get done (5 days worth in 4 days, not 6 days worth in 4 days!).
Now,if that's generally achievable is up for debate. I think most would agree 8 hours a day, 5 days a week is likely better than 10 hours a say, 7 days a week. But it's not obvious if a 30 hour week is better or worse than a 40 hour week.
Microsoft tried it and productivity shot up 40%. Yes, in Japan, but still.
After I took a solid break from work for 3 months, doing a full 5-day work week was torture. I am still not used to it, and I don't think I ever will be agin.
It all comes down to scarcity. Scarcity of time. Give me five 10-hour days and I will stretch them out by hanging out on Hacker News. Give me less time to accomplish my tasks, and I will be much better at managing a scarce resource. AND I will have a 3-day weekend to check out from work completely.
In the past it sounded very "socialist" and lazy to me, but I have come around to believe that, in the language of Mandalorians, THIS IS THE WAY.