I worked in two different hospitals who had two different approaches to holidays.
One hospital: You hired into a position that was designated as an A or B holiday schedule. One year you had one set of holidays off, the next year, the next. I think the holidays were: Christmas, New Years, Memorial, Labor day, July 4th, Thanksgiving. So one year you would have Christmas, Memorial Day, Labor Day off, the next New Years, July 4, Thanksgiving. You were stuck with this day on unless you made a person to person trade, were on sick leave or whatever.
At the other day, you just had a set schedule and if you had the day off, you had it off, otherwise it was tough luck and of course People could try to ask for the day off. I personally liked the second way the best. It just dispassionately cut the pie, but it did force supervisors to consider honoring vacation requests. In the first method, no vacation requests could be accepted and that took pressure off of the supers.