The AR, which is in the sights of Bloomberg and his ilk, is still a poor choice to go after. You are correct, it's design is not intuitive for close quarters, semi-auto for civilian and law enforcement, is made more for open combat at distances greater than what a shotgun optimally designed for. If any of the offenders in any recent mass shooting (theaters, classrooms, cafeterias, etc) had used a shotgun with #4 or 00, there would most likely be greater death and casualties despite having a larger magazine capacity and design of the AR. The attack with the highest casualty rate in the US involved neither though....
My personal opinion is that the government would like to remove the AR (including the M16 and M4) from the hands of the civilians as well as some law enforcement. Most being mil-spec it creates an almost level playing field when combined with gorilla warfare. Our government has no qualms about sending guns they find "illegal" to Mexico, then will come and take "legal" guns from away from border patrol officers.