[Broken_Hippo]

Hospitals are certainly not resting. You might not have a scheduled procedure on the weekend, but those places certainly aren't resting. Public transport depends. Airports certainly aren't closing. Taxis still run. Some places will halt bus service, basically meaning poor folks cannot spend time with family on that day - other places don't halt much at all or simply have fewer buses. Gas stations are generally open. Emergency services are open and tow trucks are available. Many places have on-call HVAC folks available (for when heat breaks) and/or emergency plumbers/electricians. Utilities still have folks on-call to fix those. In some places, a pharmacy is open due to a hospital being nearby (mostly because the hospital won't really give out prescriptions).

"A common day of rest" depends on a portion of society doing their jobs on that day of rest, not to mention the ability to do the stuff they need to do the rest of the week.

I don't even think it makes sense to have a common day of rest - perhaps save a few (3-4) holidays a year. I don't see the issue with someone wanting to not miss work for the doctor and go on Sunday afternoon instead. Nor should it be odd for a family to get together on a Wednesday afternoon. Just make sure folks have the flexibility to do these things. The individual should definitely get days off, but that doesn't mean society should stop one day a week.