After years of debate and controversy alcohol is now legal in the one of the poorest counties in the country. http://abcnews.go.com/US/wireStory/vote-legalize-alcohol-sds-pine-ridge-passes-19965000
I remember reading in a book about the problems alcohol on the Pine Ridge Reservation. Possibly the book was In the Spirit of Crazy Horse by Peter Matthiessen which was about the Leonard Peltier case. That covered events in 1975 and problems with alcohol were very bad. I don't imagine things are any better today so it doesn't look like prohibition has work so maybe this is the best way to go.
The Aussies also introduced prohibition laws in their aboriginal communities. They had a very serious alcohol problems in those communities as well.
There's a huge difference between a central government introducing prohibition and the local people making the decision. This wasn't Congress that made the decision, the reservation made it. For what it's worth, I suspect this is the better decision. The biggest reason is people can travel off the reservation to get alcohol anyway. One shouldn't minimize the problems of alcohol abuse, but using taxes to fund treatment will likely go a long way. At the same time, it's likely people will continue to abuse alcohol nonetheless.