If you expect to repel a
squad of armed "home invaders", what are the chances you
aren't going to be overwhelmed by superior numbers and weapon count, no matter how many rounds/shells your "home defense weapon" may be able to hold before having to again be loaded? Especially if caught by surprise?
Granted, none of the areas where we've lived in the last 40 years were normally subject to roving hordes of home invaders, and the rural community where we presently live is pretty much off the map for that sort of thing (unless you're dealing drugs, etc), so I have a somewhat lessened concern about such things.
As far as the shotgun loaded with "bird shot"? No personal opinion, but i do have a concern regarding misses and potential perforation of structure walls by any rounds fired (hence concern for angle/elevation of shots fired and fields of potential fire).
I once professionally met a fellow who was arrested for an outstanding attempted murder warrant (if I remember right, as it was a long time ago), and who had been shot by a local officer within a backyard during an attempted escape. The suspect was in the process of climbing over a fence, and the shotgun the officer had grabbed (from a patrol car) had been loaded with some type of bird shot (unknowingly to him, he claimed).
BTW, if you think the loading of birdshot into issued shotguns doesn't sometimes occur (instead of the issued or authorized buckshot), you haven't worked around enough cops. Cops may "run out" of issued buckshot, or have it "go missing" from their assigned veh, and quietly substitute some 12GA shells that are "handy".
I can even think of an instance where an issued 870 had to be brought to the armorer because the wrong gauge shells had been loaded into it and the mechanism locked up.
Anyway, this suspect had been hit across hit his upper chest & shoulder by a LOT of birdshot. A very large area of bandaged wounds. He told me that it had caught him by complete surprise, and suddenly hurt so much that it caused him to lose his balance and fall off the fence, interfering with his attempted escape, allowing the cops to catch him before he could get away. He wasn't a big guy, either. Fortunately for the cops, the suspect had been unarmed, so he had no way to shoot at the cops.