I think that a good deal of the issue comes from shotgun mythology.
1. You can't miss
2. It has ultimate stopping power
3. For pump guns, the racking will scare away the bad guy
4. They don't overpenetrate compared to other guns.
Here's a good take:
I've trained with both and shoot both - I go for the AR if it gets to that level of intensity.
Many of the responses we used to get about the issue were racking and posturing, without aiming as the major reasons for shottie popularity.