I think that a red dot sight is fantastic on a shotgun, if not very sporty and honest (if you want to behave like a gentleman of yore).
To give you my example, i have shot rifles and i am a better than average shot with a bullet. I guess i fired well over 20.000 rounds from all sorts of rifles. But i have never shot a shotgun in my life, and i have never learned to do any wing-shooting.
As my research project, i needed to collect 400 birds. Shorebirds (sandpipers), to be more precise, the size of a sparrow, and flying twice as fast, and very shy (if i ever got within 40 yards i was lucky). So there i was, with a 870, and not being able to collect my samples,. and wasting time by the bundle. Needless to say, after missing a shot, i would need hours to get within shooting range of another bird. On top of everything, i also needed to shoot birds at night. Now, these birds are tiny, and colored just like the mud around them, and they are quite spooky at night.
I got a red dot sight and that really made it easy for me, even though i had no experience. I used extra full chokes, 3" shells, the red dot, and i got those birds flying faster than a dove with 50 yard shots. Without the red dot i would have been in serous trouble.
Still, i guess for sport shooting like trap and skeet and such, using a red dot would not be "fair sport". But that's just my opinion, i am old fashioned.