It has been successfully tried in Europe. Main risk for the employee is that they end up working extra time in order to keep on top of their work. Technology allows and virtually demands it. By staggering the working week (not everyone gets Friday off!) the employer has full coverage.

A 4-day workweek is a wonderful, win/win, approach to optimizing capital-intensive unit production enterprises that benefit from essentially having 20-hour/day, 6-day/week coverage through the use of three groups of employees working 4 10-hour (all straight-time) days each week in schedules that slightly rotate over time to ensure that no one is continually working the weekends. I've found that, especially in times of tight labor availability, this 4-day-on, 3-day-off approach is highly attractive for staff while also cost-effectively providing higher overall weekly "up-time" for equipment/facilities (i.e., 120 hours per week vs. the traditional 80-hour two-shift, 5-day workweek. It also provides sufficient daily equipment downtime to enable regular preventive maintenance.

who wouldn't love this setup? To add to what Don Barefoot said...I have been in organizations where a 7 day a week schedule was necessary. Rather than rotating schedules as he suggests, we were able to recruit for people who wanted to work weekends as part of their work week. Many people want to be free mid week as it is easier to do things that are always crowded on the weekends. For instance we had some avid skiers/campers who found that the "outdoors" was so much more available if they were able to go to the woods in the middle of the week.
If you only need to run a 5 day a week organization, then scheduling is much easier.
As you mentioned, studies show productivity does not suffer when an arrangement like this is put in place; it just takes a bit of getting used to.
there are a few places that do a variation of this. For instance, in the summer months Nike allows all of its employees to take Friday afternoons off if they have completed 40 hours prior to noon on Friday. This has been very successful and has gone a really long way towards building morale and loyalty

In addition to the answers already shared, a four day week would be a great opportunity to define the individual culture/climate of a corporation to encourage self-care as a value. When employees are only defined by their stated roles and responsibilities, creativity is difficult to nurture. Down time well spent encourages creative, innovative thinking that comes from the recovery of positive imagination as a part of higher level thinking. It would take clear communication about the purpose and intent of the cultural shift to elevate the decision to go to a four day week as a way to contribute to the productivity and wellbeing/thriving of both the company and it’s employees.