Here's what I believe.
When there has been just a little bit of snow and the temperatures are creating a classic Spokane melt/refreeze cycle, clearing your walks just makes the footing more dangerous.
If you just leave the snow, it will fluctuate between slushy and frozen crunch. Either usually make for a survivable pedestrian experience.
But if you shovel your walk to a pristine, clear surface, you are just inviting the adjacent yard snow to melt onto the exposed concrete and then refreeze. That can create a treacherous glaze.
Of course, when there is a fair amount of snow it's time to get out the shovel.