I think my productivity would increase on a 4 day week. Less work 'days' and more practical time off.
My brothers company is trying/doing 4 day weeks for at least some of it's staff, with what used to be the third shift spread across the other two.
In their case IIRC it was a change brought about by the need to cut energy costs as they work with plastics and had machines they were having to leave "hot" for much of each shift but not running (they take long enough to clear for shut down, and to warm up again it wasn't practical to turn them off for a few hours at a time).
Apparently most of the affected staff are very much enjoying the change as it means they've always got 3 days off, and if they're doing the shift rotation they always have that 3rd day to help move their sleep patterns.
I suspect if the company tries to change back to 7 day running (which requires the 3 shifts alternating between 4 and 5 days) they'll have a mutiny, especially as by the sounds of it they got back some of the experienced staff who had previously left when they made the change.
Brother in law loves it as it means he has Friday to relax and recover a bit so can enjoy the weekend more, it also gives him an extra standard day at home to get jobs done around the house without it eating into to his relaxation time too much.
I think the downside is that he apparently works about a shift or two less a month, but that is rather offset by apparently a slight payrise and saving on travel costs.