They do think that the homes are empty for a part; others think they're stealthy.

As for the rest, no. People breaking into homes to kill or rape strangers are far rarer than you seem to think. In France, and again I have no reason to believe the situation is very different in the United States, more than 80% of rape victims knew their attacker. These are not typically people who break into homes at night. Of the remaining 20%, only a fraction involve home invasions.

At worst, that amounts to a few thousand cases per year in the United States, and probably fewer than the number of firearm-related intrafamilial homicides (which also number a few thousand, but are at least slightly more common than rapes committed during home invasions) and vastly fewer than firearm suicides.

Owning a firearm does not statistically make you safer, on the contrary. If you have enough money to buy a weapon, buy a security system and an alarm instead. They will be far more effective and much less risky.