It discriminates the very poorest alcoholics in society. Forcing them to spend more on their addiction. Which they will do. I know a few locals that still buy what would have been cheap cider, at an inflated price.
Discriminating against alcoholics is entirely the point, and they're continued poverty is in part because they're alcoholics, getting help is up to them ultimately.
As the NHS or government can't exactly find every alcoholic person out there to offer them advice beyond the usual channels (adverts or GP checkups if they ever go), that's unrealistic.