If you lived in a bad enough neighborhood and had an insurance policy like that, "accidentally" leaving your doors unlocked would be a cheap and easy insurance fraud--which is why some insurers are reluctant to cover people in that situation.
Well I always live in good neighbourhoods, so I guess the insurers don't mind in my case. My current policy also covers theft of items stored outside the house - bikes, ladders, furniture, etc.
Sometimes it's not always cheaper to live in bad areas, when you add up the total cost of living.