One drawback (and which existed in the original LeMat) is that the cylinder has to be pretty big because a shotgun barrel, even .410, is a lot bigger than the normal crane or quill. And since the cylinder is big, the frame has to be big, also. That, of course, will allow more rounds in the cylinder, but it also means even more weight.
And, FWIW, I don't want to even think about the recoil of a handgun firing a 3" Magnum shotshell.
Jim