Thanks for this post. It's good to bring attention to this as it's a big problem.
The Coconino NF website currently has some photos of damage caused by driving on roads that are not yet suitable for travel. Look it up and check out the photos. It's good education.
Obviously, travel on closed roads is a problem, but one of the most common problems is once roads have been opened but a driver encounters an area that is still snowy/wet/muddy, and therefore drives around the difficult area. I'm sure you've all encountered this before ... the road becomes 2 or 3 times wider than normal, destroying everything around the muddy spot.
If you ever encounter such a spot, stay on the road. If staying on the road is not possible for your vehicle, you shouldn't be on that road.
Two attached photos are from Coconino NF Website homepage.