All my rifles and my pistol have open sights. My smoothbore has no rear sight.
I had, at one time, peep sights and front globe sights on my Lyman Great Plains rifle. It was much more accurate for match shooting and the ghost ring was a real help for low light hunting. I sold those sights after my cataract surgery simply because I no longer need them. I can actually see the rear sight, the front sight and the target again!
Having said all that; I do shoot more accurately with peep sights. Not having a rear sight on my smoothbore helps with shooting birds and clay targets. However I am seeing two distinctive groupings on my roundball smooth bore targets. One just left of center and one just right of center. I know a rear sight would cure that, but I'm going to continue to attempt to correct that by learning to mount the gun consistently.
I don't begrudge anyone using peep sights, older eyes need them. Peeps are more accurate, but you still have to make the shot. The targets we use, combined with shooting off hand, I simply don't see a great advantage in using them.