I'm not a high-speed, low-drag kinda shotgunner... no 3-gun or tricked-out HD rigs for me... yet. However, I can see the benefit of optics in a couple of cases.
For shooting precisely at fairly small target zones (ie. deer or turkey) I can see great utility in having a sighting system you can properly zero for the load or slug you are shooting. I would guess that in some of the 3-gun matches, this would be beneficial for certain COFs.
Then again, there's always the appeal of having more/new/better/different toys... which isn't always bad.
A good friend has a 1x scope mounted on the shotgun he uses for deer hunting. The ONLY reason he uses it is because the crosshairs force him to look at the sight and line up the shot. Before using it, he had a couple misses on good-sized bucks because he was looking at the rack while shooting.
Some "tactical" folks like red-dots for CQB. I don't doubt them, but if it came down to it, I wouldn't ever bet against a guy with a well-worn 870 and a simple bead front sight.
As for me personally... optics are useless for filling my freezer with chicken substitute.