I'm out in the sticks now but used to live by a road that they used to ask volunteers to grit. I don't have a problem with sticks getting gritted at the bottom of the pile, but I'm talking about pavements next to really main roads, so used by loads of pedestrians. The sort of roads those people in cars would walk along once they were out of their cars or nurses etc might use on their way to work. They get trampled by hundreds/ thousands and turn into compacted ice. Lots of people make the choice not to go by car when the roads are bad so they need a safe alternative.
As for my road, I cleared the path for about 5 or 6 house lengths opposite my house when the snow was bad last time (basically from one corner to the next corner, but a very well used bit by secondary and primary school kids)