That could be part of the disconnect here. The target I've been taught to shoot for in a defensive situation is farily small. Moreover, in
training for defensive shooting, I've been taught to strive for a high degree of accuracy. So, for me, it's tiny patterns and tiny targets. I suppose this leads into a discussion of wound ballistics, which is way outside the scope of this thread.
In any event,
for me, placing a wad-sized payload of buckshot into a small target at across-the-room or down-the-hall distances
reliably and
repeatably requires sights.
I can do it sometimes by pointing. I shoot trap, skeet, 5-stand and sporting clays with my 870 and have a decently-groove mount. But I can't do it every time, cold, and on demand by pointing. If anything about my mount is off, I'll throw the shot if I'm trying to 'shoot where I look'.
For me, getting hits by pointing requires a very solid interface between me and a well-fitting gun. If anything about that interface breaks down (because I'm moving, under stress, etc.) I won't hit reliably. When I miss a bird on the sporting clays field, I can often attribute it to a sloppy mount.
Using sights eliminates the need for a perfect (or near perfect) mount. If I do my part, I can get accurate hits on the move, on my back, from the weakside shoulder, etc. using sights. That's simply not possible for me by pointing.