YES, new cars are safer.

[prosperity]

Five years ago, this was a little narrow 2' wide ditch and now it is over 4' wide from all the cars going in it and scraping the dirt from the sides. I wonder if there is any practical way that the highway department could fill the side of the ditch to make it narrow again. I don't want them to put a culvert in the ditch because the ditch stops the cars from coming in my yard.

When I used to work for the highway dept. here, we had a lot of ditches that were way too deep, mostly because of yearly ditch cleaning.
What we did is semi-filled the ditches with #4 limestone. This still allows the water flow while reducing the depth/width of the ditch.
Our foreman would coin the phrase "drive in - drive out" of the ditch to give you an idea of how much we filled them.

Contact your state or township highway dept. - maybe they can do the same for you.