My horse has a braided tail in a tail bag but he also has a fly sheet, gets treated with fly spray and we don't have a fly problem at our barn to begin with. He's never seemed distressed or uncomfortable and certainly is not being pestered by flies. Call the humane society, he's probably abused because I do things differently than a handful of people on an online forum
I think it depends on where you live and what else you do to keep your horse comfortable and fly-free. If your barn/pasture is swarming with flies and your horse has to constantly be swatting at them, maybe you don't want to braid but you probably also want to do something else about the flies too.