It's not really going to help the people that most imagine when they think of their personal experience of homelessness. i.e. people sleeping in the streets or on the subway, or the "crazy people" you cross the street to avoid.
For example, in NYC, more than 95% of the homeless are actually sheltered (whether in the city shelter system, or in other temporary situations like doubling up with friends or relatives), and more than 80% of homelessness is situational rather chronic. 30% of homeless families have at least one employed adult. 60% of all shelter residents are families.
Most spending on combating homelessness is invisible to us; and most improvements in affordable housing are going to have little impact on the (predominantly) male, drug-using and/or mentally-ill street sleepers.