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so the continuity of care does play a role in that. But it's also because hospitals are cheap bastards and longer shifts reduces staffing requirements.
a traditional 5-day work week with 3 shifts per day, on a 24/7 operational time results in 6 full shifts plus staffing for covering absences. A 12 hour shift a/b, c/d rotation has four full shifts plus coverage, just as an example.
I didn’t understand the math in your second paragraph. Could you explain again? I don’t have any prior familiarity with shift planning.
I'm going to use a 24 clock here, just to make it a bit more obvious. (am/pm is annoying on a 24 hour rotation.)
most place use something like a 09:00-17:00 shift. (or 07:00-15:00, etc.) "full time" is 40 hours a week in the US, and we get there working five days a week (monday through friday). For types of jobs that go 24 hours a day, 7 days a week, that falls into three shifts- First shift starts ant 09:00, second at 17:00, and third shift starts at 01:00
for every position, if you want round-the clock coverage, Monday through Friday, you typically have one full time person for each shift. 3 people. You then have shifts on the weekends- Saturday and Sunday; because overtime is a big no-no; that's another 3 people. So for a single position, working "typical" 8 hour shift rotations, you're going to need 6 people. (and, 3 of them are going to have high turn over as they move into positions that are full time. which can be quite problematic.)
one way of doing things differently is to have four shifts that are 12 hours long. A/B and C/D are paired together. A and C are both day shift and B and D are night shift. the two pairs alternate between 3 days on and 4 days off, and 4 days on and three days off.
because there's no part-timers on the payroll, it reduces overall turnover, and the contingent costs associated with onboarding. you've also cut your on-going continuing education costs by a third. when you're talking across hundreds of nurses, that actually adds up enough to justify the 4 hours of overtime everyone gets. But even that can be avoided- many places that technically have a 'you must be paid overtime' frequently have exceptions for 12 hour shift rotations. (which generate an extra 4 hours of overtime every two weeks, in this example)