Perhaps they just really like alchohol. If people are happier while drunk, is wanting to always be drunk really that irrational?
That said, while even the best of people aren't perfectly rational, even the worst aren't perfectly irrational. People won't respond right, but they will respond.
They might even respond too much. They might decide they don't need to stop drinking because they can go to a wet house, even though they're unlikely to be accepted.
"Wet houses"-- subsidized housing for alcoholics (they need to get most of their own money for alcohol, but their other expenses are covered) might actually be a good idea. It's cheaper than trying to get them to stop drinking, arguably kinder than trying to get people to take on a very hard task that they aren't interested in, and leads to less collateral damage than having alcoholics couch-surfing or living on the street.
Utilitarians, what do you think?