It may be that many, if not most, could give up alcohol if they feel inclined to, but whether they should is a different matter: for me 'could' isn't a synonym for 'should' in this case, and while some people perhaps 'should' forego alcohol in certain circumstances, say for health reasons or because they are due to drive, I'd say that it is primarily a personal decision for (alleged) adults to make.
Speaking personally, I could give up alcohol but choose not to.