ninared 60 children were killed and 2352 seriously injured on the roads in England alone in 2011 - a normal year.
You don't see that in the media because it happens all the time, unlike the shocking cases you refer to that hit headlines very occasionally by comparison. Road accidents are the leading cause of death for children and of spinal injury, loss of limbs and head injuries. 2/3 of the deaths are to pedestrians killed by cars.
Statistically the OP's child would have been safer in bed than walking to school with her mum.
Of course it depends on circumstances and should be risk assessed (as I referred to in my earlier post) but your post is based on emotion not any kind of logic.
Doing things that make your life awkward and your children's lives uncomfortable doesn't automatically make you a better parent - sometimes the difficult option is the better one, sometimes it isn't (no need to take the difficult route of gathering wood and rubbing 2 sticks together to light a fire - go ahead and take the easy way out, just switch the heating on :o ).
Allofthe sorry, you didn't predict a horrible death - somebody usually does though :o If I broke my risk a 15 minute walk from home I wouldn't want my ill child sitting in the cold with me either, though of course it would be better than him or her witnessing my death under the wheels of a car. If I should be delayed my child at home can call me, and if I am incapacitated and don't answer they can call one of several other people, or if necessary pop to one of several neighbours houses. If I broke my wrist I would have to contact somebody to take the children anyway, whether they were with me or at home... easier to call one of several neighbors who wouldn't even have to get in the car to go and get them, and then call DH to set off for home...
Obviously if the child is so clueless they'd just hang around the house wondering what to do they are not ready to be left - but if they've got anything about them you've built up to leaving them gradually over time they won't be remotely thrown off by needing to call one of the well known people who can help - dad, grandparent, neighbour etc.