Without wading into the "good guy with a gun" debate, tl;dr: almost no humans want to effect the level of violence required to execute a home invasion, even if the risk of being shot is zero. A big deal is made about guns as deterrents, but the simpler answer (and the one that explains why it's also safe in rural areas of other OECD countries with gun control) is that humans just aren't that violent--when there's enough to go around anyway. That's all I'm saying here.