There's a really simple solution to this problem, and it doesn't involve firearms.
Here's a really great breakdown of household burglaries.
In cases where individuals were home and victimized, 65% knew the offender. That's interesting.
But the really interesting part is Table 7. In 77% of burglaries, in which the homeowner was present, the offender gained access through the following ways: Someone let the offender in, Open door or window, Unlocked door or window, Had key.
We could virtually eliminate household burglaries while the homeowner is present by using a little bit of common sense. Lock your doors, keep them shut, don't let strangers into your house, don't give out keys to people. And of course, a functional alarm system. No firearms necessary.