At some point, the three foot depth is needed to collect rain water runoff and move it to a lower point. The ditch in front of my house is only about six inches deep at one end of my property but it gets deeper further down the road, before it goes across a field and into a large pond. I would rather than the county engineers have it three feet deep in the correct places than to have my property flooded from water running off the road onto my yard!
I trust that the county engineer's crew knows how to manage the location, depth, and slope of the ditches correctly, along with size of culverts and location of culverts that run under the roads, to prevent or reduce flooding of roadways and properties.
By the way, your whole yard isn't 3 feet below the road, is it? It looked to me like it runs significantly uphill from the road.