Here in Seattle I've been held up for over an hour on the 520 bridge because of an accident THE OTHER DIRECTION. Having screens would prevent rubber necking on the other side of the highway (with a large cement barrier in between).
Also, I think you can do a lot to the screen itself to increase driver safety. Make it 15' high and entirely yellow/black diagonal stripes and it'll catch driver's attention and get them to slow down. TV and radio educational ads can help too.
The article also mentioned that because of the spectacle, drivers are paying less attention to the road and looking at the wreck, causing secondary accidents.
Then again, a tarp with emergency vehicles is another reason for drivers to slow down and look at something, according to the article. The trick is to find something so mundane that drivers won't bother slowing down.