The real economic drain comes in health expenses. Many houseless have no health insurance, and emergency room visits are a huge expense. Living in the rough is unhealthy and most the average year of death of houseless folks is 48, before that end, many have expensive procedures.
It is considerably cheaper for a society to provide housing than to treat people who live on the street. The economy would improve, and we would have more citizens involved in our community, if all who wanted to be housed could be.