Grass unless it is too shady. Then geranium macrorrhizum has done well for me against plows.

You may be able to get away with planting some things against the wall, so long as they are salt resistant, and can handle being cut down to the ground.

Don't get into a battle with the plows. They will win.

Depending on the look you want, there are many native plants you could use. They are attractive while helping out the environment. If it's sunny you could have a pollinator garden, especially butterfly milkweed or common milkweed. Both are hardy and salt tolerant, if your road is salted. You could also go with a native or grass. Little bluestem or prairie dropseed are both easy to grow and tough as nails.

I'd go with a micro clover.

Pussytoes, creeping juniper. We have grass. It recovers pretty quickly, although our strip between stone wall and road (with hemlocks) is much steeper, so we tend to get gouges.

My house has the same problem with plows. Worse, the DOT salts the road when there's a thread of snow or ice! So the runoff kills pretty much anything.

I LOVE your wall, though! So there's a lot of potential here.

After trying a million things, I ended up just using mondo grass. That stuff is indestructible!! I've sprayed it with Round Up, and I swear I can hear it laugh! LOL It's good in sun or shade, and I've never watered it once. I don't even plant it; I just dig up a bunch and sit it where I want it, and it will root itself.

https://www.monrovia.com/mondo-grass.html

My suggestion would be mondo grass along the base of the wall, and then dwarf mondo grass to the road if you can find it.

You can then plant annuals between the mondo grass in the Spring. And since they'll die at the end of Autumn, anyway, there's no real loss over the Winter.

Only downside is that, maybe one a year, you'll need to take a shovel down there and dig up any of the mondo grass that's outgrown where you want it.