In addition, drunk driving is a relatively controlled problem. That is, a relatively small percentage of the population do it and law enforcement is able to police it with a reasonable degree of success. On the other hand, it we had an epidemic of drunk driving where say 20% of the people on the road were driving drunk then it very well may make sense for the government to barricade the roads until they got things under control.
And yet you argue that allowing free commerce in America is not okay with a population that is dangerous to a relatively small percentage of the population.
Edit: Found this as a support source, while not 20% roughly 2x the rate in rural vs urban areas https://www.ncbi.nlm.nih.gov/pubmed/30160320