It depends on the horse and on the rider, honestly. Some people always boot, some never do. Some horses interfere and need boots, others don’t. I tend to fall on the always boot side of things mainly because I’ve had horses who really need protection from themselves and got into the habit.
My now retired horse was a genius at hurting himself, so he always went out in a full set of everything, and wore bell boots 24/7. On my jumper, I don’t have to worry as much, but I like to protect his legs. I don’t bother with fleece polos since they seem sort of worthless to me, but I will sometimes use the T-Sport wraps from Equifit if I am just flatting. In the winter I use the woolback Valena boots for flatting when it’s cold.
The rest of the time I have a few different sets- my favorites are the Veredus Carbon gel open front and ankle boots. I only use bell boots on my guy when we are in grass or showing, since in grass he will sometimes just slide his front shoes off with his hind feet. In jump offs anything can happen and he once grabbed his heel pretty bad, so we wear bell boots or quarter boots for the ring.
As long as whatever you use fits well, doesn’t hold in the heat, and doesn’t inhibit the horse, use whatever you like. One caveat: I really dislike the Professional Choice Sports Medicine boots, or any kind like that with the thick neoprene that wraps all the way around because I’ve found that those heat up the leg to an alarming degree.