Caro, you imagine so many awful things happening, how do you sleep at night?
Yes, something dreadful could happen, but it could happen to any of us, at any time. The chances of those things happening are very slim, and even more slender if you are co-inciding them with just the moment you step out to run an errand leaving your child alone.
Life is full of risks. Any mother could fall downstairs while carrying a baby or toddler, on any day. It does happen, but rarely. Mothers don't refrain from carrying children on the stairs because of that risk. Similarly, most of us travel by car/bus somewhere nearly every day. The risk of accident is there, but we judge it a risk worth taking, given the chances, and the advantages travelling by car gives us.
Some parents feel comfortable leaving a 9 year old (or younger). In 99.9999999% of cases they will be fine. and the other 0.00000001 case? well, maybe mum wouldn't be able to get the child out of the burning house anyway?
Personally, I'd rather leave ds watching Ben 10 for 10 minutes, than spend 20 minutes persuading him he needs to come with me, then have a car accident cos he's distracting me cos he's grumping at having to come with me.