Initially, there was a problem making incendiary ammunition small enough to be fired by standard British Army weaponry (i.e. 0.303 inch).
This is why single shot Martini-Henry rifles (as used in the Zulu War !) were carried by anti-Zepp fighters, as the standard infantry Martini had a calibre of 0.45 inch (leaving an exit wound you could put your fist in to, apparently).
Presumably, the advantage of using a shotgun was the spread of shot which meant that aiming didn’t have to be spot on (I have read that Cody used birdshot for his trick shooting for the same reason).