The article goes into this in great depth on both sides of the issue, but this is probably the most direct answer.

The drinks, dispensed by nurses as a form of medication, are meant to prevent the clients from becoming overly intoxicated while avoiding the worst effects of withdrawal, which may lead to seizures and can be fatal for those physically dependent on alcohol.

To address the “taxpayers expense” part, it’s way more expensive to provide major health care than small amounts of vodka.