I think it all comes down to what works best for each individual horse.
Most horses don't need to wear a fly sheet. Sometimes their owners use them anyway if they prefer to try and keep their horses coat clean and protect their coat from sun bleaching, not have to use fly spray and things like that.
Some horses are allergic to fly bites and/or fly sprays, so a fly sheet would be a very good idea for these horses to help protect them from the flies, especially if fly spray isn't an option because of allergies to it.
I have used fly sheets on my horses in the past. I honestly think they are happier without them, I just have to make sure to apply fly spray before they are turned out. Their coats aren't as nice, but I think they prefer not having to wear the sheets.