From https://en.wikipedia.org/wiki/Soviet_calendar#Five-day_weeks :
"Eighty per cent of each factory's workforce was at work every day (except holidays) in an attempt to increase production while 20% were resting. But if a husband and wife, and their relatives and friends, were assigned different colors or numbers, they would not have a common rest day for their family and social life. Furthermore, machines broke down more frequently both because they were used by workers not familiar with them, and because no maintenance could be performed on machines that were never idle in factories with continuous schedules (24 hours/day every day). Five-day weeks (and later six-day weeks) "made it impossible to observe Sunday as a day of rest. This measure was deliberately introduced 'to facilitate the struggle to eliminate religion'".[25]"
See also https://www.theatlantic.com/magazine/archive/2019/11/why-don...
A 2-day weekend, with one day/half day off during the week for appointments, would be a much better system. The employee could select the day themselves to suit their preferences.
It makes no sense that everyone gets the same two days off. It is such a hassle scheduling doctors appointments, receiving repairmen, going to the DMV, etc. on a weekday.
The only reason we have the same two days off is for historical religious reasons. And a rolling schedule could still accommodate that for those who care.
For everyone else, just put them on a rolling schedule of five (or four) days of work per week, any days, with some predictability.