That cycle of shifts (or similar) has been worked for years. It is liked because it is effectively 4 on-4 off. Attempts were made to bring in a roster (prepared by physiologists) that worked opposite to that ie start early when you are freshest at the start of the cycle, starting progressively later as the cycle progressed to give you time to sleep in etc. and counter fatigue build-up. Noone wanted it because it meant you only got 2 days off (same as every one else).They then tried to move the doggo to the next day to avoid the short turnaround. Same problem. Eats into your days off, noone wanted it.
"Now in my group, most of the controllers have to work all night, every six nights, week after week"
It's called shift work. Most shift workers on a rotating roster would love only one night in six. And to be honest, it's not really ALL night is it?