Banning alcohol may be a good idea, but it seems infeasible. Last time the US tried it, it didn't go well.
There is also hardly any accommodations for people to go out drinking outside of walking distance from you home (especially in rural areas; it might actually be safer for you to drive in a protected vehicle then risk being hit by a drunk driver on your bicycle). And to top it off, the police it self is really dangerous, so it is hard for friends or bartenders to justify calling the police on a drunk driver.
All this makes a perfect environment for people to rather “risk” drunk driving, which as we know is a disaster. I think banning alcohol is a terrible idea, providing accommodations, better enforcement, friendlier law environment, etc. will go a long way.