I don't believe it's a deliberate decision by (most) policymakers. I think it's a structural failure across several axes, including failure to make enough housing for it to be affordable, and attacks on every front by people who treat all social programs and public assistance as evil. Most places have one or the other problem, if not both.
A drug-addicted/mentally ill chronically unsheltered person is not going to be able to afford a home at any price. If they could hold down any kind of regular job and sustain an income they would find someplace to live.
Also most "affordable" housing initiatives attack it by mandating "affordable" for new construction instead of just letting developers build what they can make the most money building. No developer wants to build "affordable" homes if they can build and sell high-end homes. So by imposing "affordability" mandates, they just encourage developers to go elsewhere.
New high-end homes make the older homes more affordable. New "affordable" homes simply don't get built, at least not in anywhere near the numbers that are needed.