Hahaha. Big ooft. Would mean that mostly those who can't access healthcare or are not rich are able to control magic/left to develop this 'organ'. So 3rd/certain 2nd world countries and America.

Your biggest problem with this, particularly in the emergency departments, is the sudden onset of emergencies, their scale, and the time needed for certain surgeries/procedures. There are times when you, as a medical practitioner, need to be on for the entire period that it takes to resolve the onset of cases before you because any switch-over will result in loss of information and potentially death. With so many emergencies happening all the time in a larger population/operational radius of the hospital it become untenable to keep to that kind of schedule consistently and any inconsistencies results in a cascade effect across rosters/schedules.

It's good to at least attempt to keep to that kind of schedule and it makes sense to try it at least but ultimately it is impossible to just say "this is the solution" for every scenario.