I've done a lot of volunteer work with the homeless and learned a lot from social workers in that field. There tends to be three categories that the homeless fall in to.
1) Temporary homelessness: those that have experienced a major economic fallout. They tend to be homeless for about three months before stabilizing and finding a home again.
2) Long term homelessness: those in this category tend to be dealing with substance abuse
3) Chronic homelessness: the people in this category almost always have some severe mental disability. Most people in this category have case workers who even help them find housing yet it is still difficult to keep them in that housing.
It's not as simple as more money or more housing. Although the article's suggestion may work for the first two categories it won't work for the third category. The third category needs better medical care.