The agency I just retired from after almost 32 years on the job works that schedule, 4 on, 4 off, 3 on, 3 off, 12 hrs shifts.
The three was not bad, but the 4 on was a pain in the ass.
We switched days to nights, every three months.
Every 4th week, the sergeants on the shift would switch weekdays to weekends.
That was 4 on, 4 off, 2 on, 2 off, 3 on, 3 off, then on with the rotation.
As a sergeant, you did not know what your schedule was, other than watching week to week, especially on nights.
Then toss in meetings, training, court, you never had any time off.
The officers have an extreme dislike for the 12 hour shifts, with the only caveat that they "like" the 4 days off. The only issue is that the way the shifts are set-up is that you move to your 4 days off after night shift, so in essence you only get 3 days off.
I do not like that schedule, and think that 12 hr shifts are a hazard.
The reason we had to go to that shift was a senior administration decision, which was based on the previous " city managers"decision to cut two patrol and two detective positions.
We went from a force of 14 sworn to 8 patrol, and one detective.
The reason for the cut was the former "city manager", at that time, was on a single 3 year contract, with no renewal, who had no previous public administration experience, and disliked law enforcement by his own admission in public, who was flexing his muscles based on comments from the bar owners and shitheads in town.
That was 4 years ago. The personnel cuts to this date have not been recovered.
I am glad I am out.