I think I qualify as an old-timer at this point (and I happen to be an old lawyer), and I, too, have never heard of anyone whose active alcoholic ex got sole custody. Remember, too, that even shared custody often refers to shared LEGAL (rather than physical) custody. With young children, unless the parents live in very close proximity and are CAPABLE of the level of cooperation required for shared physical custody, one parent usually has primary physical custody and the other parent gets "parenting time." When I divorced my first husband, we were in complete agreement that he would be the primary custodial parent for our two young boys (grade school age)--he had the better parenting skills (and had been sober 15 years). We had a very cooperative arrangement and set up a basic schedule, which we adjusted as appropriate. Ours was an unusually cooperative situation, but even so, I lived in a separate school district and it would have been difficult to have a 50-50 living arrangement. Tough on the kids and tough on us. If we hadn't agreed, I doubt the court would have forced it on us. The court would probably have made one of us the primary custodial parent and the other would have had parenting time--exactly the result we arrived at, ourselves.
There are several people on the forum that have used sobriety monitoring or supervised parenting time to protect their kids when they are with the alcoholic parent.