Unintended Consequences of Stop Signs

The latest edition of the Atlantic Monthly features an article by John Staddon, a Professor of psychology and brain sciences at Duke University. The article discusses some of the differences in how the US and Britain regulates traffic and how there are unintended consequences to over-regulation.
Distracting Miss Daisy:

I began to think that the American system of traffic control, with its many signs and stops, and with its specific rules tailored to every bend in the road, has had the unintended consequence of causing more accidents than it prevents. Paradoxically, almost every new sign put up in the U.S. probably makes drivers a little safer on the stretch of road it guards. But collectively, the forests of signs along American roadways, and the multitude of rules to look out for, are quite deadly. Economists and ecologists sometimes speak of the “tragedy of the commons”—the way rational individual actions can collectively reduce the common good when resources are limited. How this applies to traffic safety may not be obvious. It’s easy to understand that although it pays the selfish herdsman to add one more sheep to common grazing land, the result may be overgrazing, and less for everyone. But what is the limited resource, the commons, in the case of driving? It’s attention. Attending to a sign competes with attending to the road. The more you look for signs, for police, and at your speedometer, the less attentive you will be to traffic conditions. The limits on attention are much more severe than most people imagine. And it takes only a momentary lapse, at the wrong time, to cause a serious accident.

The tragedy of the attention commons concept reminded me of a video I recently came across on youtube called “Awareness Test.” In fact, the article refers to the video in the final section. (warning: you must actually count the passes for the video to have any value):

So what am I suggesting—abolishing signs and rules? A traffic free-for-all? Actually, I wouldn’t be the first to suggest that.

I believe that U.S. traffic policies are inducing a form of inattentional blindness in American drivers. When so many drivers say, after an accident, “I didn’t see him,” they’re not all lying.

How would this be handled in a system of private roads? I imagine the road operator would set signage to optimize safety and minimize lawsuits. Any disruptions in traffic flow would be certain to hamper revenues while accidents are investigated and cleared away. In intersections between different operators, the options are endless, but more critical. The operators would have the incentive to cooperate to enhance their own revenues and keep accidents low.
But, would the private system be plagued by the same “tragedy of the commons”, as individual operators seek to minimize its own losses by posting signs?