We only had one car, and, I am not convinced that "special tags" would have kept my folks from driving -- drunk or sober. I do know that, as a (always sober) teenager, I would have been mortified to ride in (much less drive) such a "tagged" car.
Alcoholics don't live "in a vacuum"; they do more than enough mental damage to their families. Why add to it with "feel-good" stigmatizing legislation?
My dad was a drunk, so I certainly understand what you went through. And I agree that drunks are unlikely to be motivated by a license plate. However, the drivers around him would be warned of his potential threat, and cops would have a better chance of keeping him off the road, possibly saving someone's life.
So I think this legislation is actually useful. But if you disagree, I'm very willing to hear your reasoning.