I don't really know much about the school run where I am living now as I don't live close to one and have no cause to go to a school. However, where I previously lived in London, the nursery school just around the corner worked very hard with parents to discourage the use of cars and to ensure the safety of pedestrians, including the children. A new secondary school was being built at the time that I moved and has, I think, opened this September. They also were developing a policy about parents delivering their children by car and encouraging cycle use. While it is not strictly speaking the responsibility of the school to "organise" the journeys to and from home for the children, I think it is helpful if they discuss safety issues and a travel policy with parents.
My family has had a dire warning about young children running ahead along the pavement. My cousin's eldest son was doing just that with his father only a little behind him, when he spotted a friend the other side of the road, ran across to see him, was hit by a car and killed instantly. A lovely boy gone in seconds and no amount of bellowing could have prevented it. We have all since been especially careful with our own children. So, no, maundymoney you are not being at all unreasonable.