In a home invasion I would have thought the last thing you would want is a gun. If you're in the US, then the invader likely has a gun, so if you also have a gun then you're giving them a pretty good incentive to shoot you. If you don't then you might get robbed, but home insurance will cover that.
I have the strong suspicion that in the majority of home invasions in the U.S., the intruder does not have a gun. I think that most are unarmed (to be armed and caught is a much, much worse situation), and most do not intend to encounter anyone.
