I've used fly sheets for years, even in our hot, humid climate.
The only brand I will buy is the Kensington. One gets what they pay for, and these are the only ones that hold up year after year to my horses, even Chivas who is super hard on everything!
On dark horses especially, IME, they stay cooler with the fly sheet than without. They also stay cleaner. There was a time, when I was showing, that my horses lived in some sort of sheet/blanket 24/7 nearly all year without any issues.
I have the typical fencing in the area, barbed wire, which is hard on sheets and blankets when horses are reaching over the fence for the pretty green grass on the other side
Since there are cows down the road from me, even with a feed-thru-fly control I still get flies so also hang fly traps and spray if no sheets are on. Lacy will most likely need a fly sheet as her skin has issues I haven't been able to resolve yet
Kensington makes two styles of the fly sheets, a European style which has longer sides and is more squarish, and the American style which is longer backed and shorter sides for QH type builds.
They do feel super stiff at first, but on a horse in the warm quickly conform to their shape. Some rain gets in, but not as much as one would think.