OK, I don't have any experience with a straight 4 day school week, but for one year in high school we had something that highlights the problems of a 4 day week.

We had a schedule that had 5 periods meeting for 70 minutes FOUR days a week.  One of these classes was a "floater" class.  On Monday the floater was skipped and the other 4 classes met.  On Tuesday the floater replaced the last period.  On Wednesday the floater replaced a different class, etc.  The floater just met earlier and earlier in the day as the week progressed.  There were a few 45 minute classes in our schedule that met every day also to fill out the day

The problem was, being you met less often, it caused problems with homework.  Teachers had to cover more ground and assign more homework.   Any kid that was confused got further behind because more material was thrown at him/her and less class meetings meant less time to catch up.   Teachers felt you could only throw so much material at a student every day and they needed time to process it with homework.

The students really didn't mind the system but teachers hated it and were adamant that they covered less ground than normal and demanded the district go back to a conventional schedule.

I realize I probably have a lot of confused people trying to figure out how this worked and how it relates to a four day week and I apologize for that.   But the point I'm trying to make is it didn't benefit the students.