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The thing about insurance is that it isn't supposed to be statistically sound and right most of the time, because it involves events that you don't get to repeat 100 times until you come out ahead.
It involves low probability events with very high impacts. Your house probably won't burn down, you probably won't crash your car, and your kid probably won't get seriously sick/injured. But you insure for all of those.
And you don't insure for the "most likely" event within that subset: a pan fire that scorches a wall, a fender bender that will leave you with a bruise, or stitches for your kid. You get a fire extinguisher, have a plan that'll cover your whole house burning to the ground, wear a seatbelt even a block over in the neighborhood, and get health insurance that'll cover an exotic cancer that needs a million bucks in treatment.
99% of the time you won't be attacked. If you are, statistically you'll brandish and the coward will change his mind. If you do have to fire, statistically it will be a couple shots and then over. But I don't want to be protected in "most" cases, because you don't get a do-over.
Thugs tend to travel in packs, and there are plenty of cases of multiple home invaders, muggers, etc. If the worst of the worst happens, you want all your boxes checked: airbag AND seatbelt, insurance for cancer AND organ transplants, cell phone AND flashlight AND full capacity pistol.
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