Wing plows are fairy common, although not so much in cities. Wing plows are used throughout the storm and you are correct once the snow stops crews will then use the wing plow to push the snow further back off the shoulders. Once the banks get high enough many crews have a wing plow on road graders and those will both cut the banks down and/or push them further back. Here's an example, yes its from Sweden, but it happens throughout the US in snow country as well: