if they had a felony criminal background, as in a violent crime on their record, they cant own a firearm anyway. What crime can you think of that "alcohol is a major factor" that isn't already a felony... or which isn't a valid reason to remove a constitutional right? I don't think your proposed law would make any difference. It's like the "no-fly-list" bans... no one who has committed a mass shooting in the US has been on a no-fly-list. A law that doesn't protect the public from any measurable harm is unlawful by definition.