To play devil's advocate (and weather the downvotes for doing so), alcohol doesn't drive drunk, and most people who use it do so responsibly.
If a bunch of peeps who don't drink wanted to stop drunk driving, they would see the best solution as just banning alcohol. Its a simple solution and makes sense. Nations like saudi arabia have banned alcohol and have significantly less drunk driving incidents. It wouldnt make sense to them why so many people would resist such a simple and proven solution. If they won't ban it all then atleast ban the liquor, etc.
Meanwhile the people who drink responsibly wouldnt want to have to give up drinking just because a few idiots drive drunk. They would see the best solution as finding ways to stop people from choosing (or being able) to drive drunk, while still allowing themselves to use it responsibly, but that is a much harder thing to do.