they wouldn't use a shotgun because it takes longer to reload
You can get box mag fed shotguns, with like 20 round mags
The issue is that 12 gauge shells are significantly larger than pistol or small caliber rifle cartridges.
The determining factor is concealability. Most shooters either grab a pistol for that reason, or they say "I want to use what that other guy used" and grab an AR-15.
(Fun fact: the Parkland shooter used 10 round mags specifically because of concealability. And yet March For Our Lives is still pushing to "prohibit the sale of high-capacity magazines such as the ones the shooter [used] at our school" because forget research and correct facts, right? Why have that when we can have bullstuff propaganda instead?)