Bricks, Masonry, Asphalt and Concrete - backfilling around asphalt edges

We just had our driveway asphalted. We just had a gravel driveway before. It was very low and needed to be built up and graded before asphalting. I also wanted the asphalt to be fairly thick because of where we live and the amount of traffic on it. The issue? The asphalt looks great but it is several inches above the ground/grass. The contractor did a great job sloping the edge of the asphalt to the ground so that we can run our lawn tractor easily over it. This also helps with water run off. I think it would look even better if next spring I had it backfilled with dirt over the sloping areas at the edges and then reseeded with grass seed. This would bring the grass flush with the asphalt. I have not seen this too often so any suggestions would be welcomed. Any other ideas? Is this common?

I'd let it go for a couple seasons - the loose dirt tends to accumulate there and build up over time anyway.