Yeah, and I'd like to see a scientific study about this to show how it works and so people can understand it. A significant amount of money is spent on clearing and treating roads during wintry weather, I think it would be very beneficial to understand why taxpayers spend this money and what they get in return.
Additionally, if information such as "winter tires are X% better at stopping/turning than all season tires when treating roads with Y" could be presented, then maybe more people would opt to purchase winter tires (or maybe the opposite) depending on what types of solutions the local government uses.
A brief google search brought up a PDF for winter tires from the traffic injury reduction foundation, with the basic conclusion that yes, they are better, but updated studies are needed for exact numbers.
Walk into any car tire store, and you will see displays for winter tires claiming anywhere from 25-35% improved stopping distance. Of course, with less frequent plowing, salting and sanding, these numbers likely go out the window. They get you better stopping distance, but they aren't magic and it is still worse than all season tires on a dry, summer road.
If you want safer winter roads, you use salt and / or sand and plow every time significant accumulation of snow occurs.
I drive on unplowed paved roads and I can tell you from first hand experience that there is a world of difference between snow tires and all season tires. The chemistry of the tire itself is different. All season tires start getting hard around 40F whereas snow tires stay soft/rubbery below 40F and colder. This is fundamentally why snow tires are superior for snowy/icy conditions. This is also why you should not use snow tires in summer because they will wear very fast due to the composition being soft.
Additionally, if information such as "winter tires are X% better at stopping/turning than all season tires when treating roads with Y" could be presented, then maybe more people would opt to purchase winter tires (or maybe the opposite) depending on what types of solutions the local government uses.