I have some experience with this.
My 2002 Camaro SS was a square fit and handled superbly on a smooth track. And, I could rotate the tires at will. I never had car shake and you couldn't tell which tire it was from, but rode in many of them ... all with staggered fit. The staggered guys didn't have anything on me in corners. Earlier in my life I had several staggered-fit cars. I loved them all until it was time to buy tires.
Cut to today and I have a 2019 Ford Mustang GT Premium PP1 on order. I am going with a square fit ... 285/35R19s and SVE SP2 Bronze wheels. I have heard others say they aren't wide enough, but they are. Without a ruler or looking at the sidewall numbers, you can't tell if they are 285s or 305s, even parked side by side.
Rotating the tires has tremendous advantages and zero disadvantages unless you are just one of those guys who likes a staggered look on the street. It's fine of you are driving a T-bucket and has no downside until the first time you have to buy tires. Then you wind up with old rears and new fronts or vice versa, and the handling changes. It can be very tricky in rain.
I'd stick with a square fit and enjoy a smoother ride all through the car's life after the first tire change.
However, in the end ... it's YOUR car and only you can make the call. I like the staggered fit look but have made a choice after experience with it. if I had an old Dodge Charger, I'd do a staggered fit just so it would look good. In a new Mustang GT, I'll go with a square fit.