Traction certainly does help in stopping and turning by keeping the tires rolling so you will still have control . Especially with a FWD car asking the front tires to drive and steer is a receipe for trouble, you loose traction and you have lost all control.
The biggest advantage to a pure snow tire is added traction on ice, there is not much difference between an all-season and a snow tire in snow.
I have been driving in New England winters for 40 years and adjust my speed and following distance to the conditions. I have had only one instance back when I was a teen and spun out in a corner and got stuck in a snow bank. The folks that scare me are the ones running around with bald tires in snowy and icey conditions. I don't think legislating snow tires will help with the clueless folks you meet on the road.