If plow drivers would have to do this and not angle their blade every time they got to a driveway while making sure to not push snow into the other lane (and into oncoming traffic), then it would take them so long to get roads done people would have to drive on unplowed roads constantly. If plows don't get fresh snow off roads quickly before too much traffic gets on it, particularly on side streets, driving becomes a nightmare.
My home here in MN is on a hill, so I have to keep my steep driveway clear as much as possible if I have any hope to get my minivan or small SUV up it and into the garage each trip. So, during bigger snows I try to do what I can initially to make my driveway usable to get cars in the garage for the night, then I put the shovel away and wait until I hear the plow roll through early the next morning - and quickly get down to where they push my driveway shut to clear that out before the slush/disturbed snow solidifies. If you let that stuff sit even for an hour, it's like concrete - especially in really cold temps.
My advice would be to try and time it as best you could to leave the bottom of the driveway untouched until the plows roll through, so you only have to shovel it once - and do it quickly. Or, make friends with a retired guy on your block with a shiny new snowblower and he'll bail you out a time or two!