I found this as well. In fact, I've recently turned off the iron sights feature - I find it really difficult to target the enemy using any gun that is not tailored for this. I'm talking Caravan Shotgun, Lever-action Shotgun, 10mm pistol etc. Only weapons like the Service Rifle with an actual sight make this feature workable, otherwise you're just guessing where the enemy is behind the barrel of your gun.
I know the Caravan Shotgun is bad but I can pick off targets with the 10mm Pistol at 50 yards easily, which is the maximum distance you'll usually find in a building. It makes it an invaluable sneaking weapon thanks to the silencer. The weapons I've used and have been accurate with thanks to the iron sights are:
9mm Pistol (without scope)
10mm Pistol
.357 Magnum
.44 Magnum
Hunting Revolver
Service Rifle
Assault Carbine
Hunting Rifle (without scope)
Cowboy Repeater (incredibly accurate for such an old weapon)
Trail Carbine
Hunting Shotgun
Single Shotgun
I think that's it. I didn't include weapons that had scopes because... Well, that's not aiming down the iron sights is it? I was surprised that the Single Shotgun was so accurate, but not so surprised by the Hunting Shotgun (hunting firearms are accurate by design).