Why should issues like homelessness be reducible to one 'primary' cause?
Highlighting housing costs as a significant contributing factor is an important point to make, but there's no need to undermine the other contributing factors through bad faith arguments and cherry picked statistics. Yes, homelessness clusters in cities with robust social programs, esp. those with temperate weather. These same cities are also the most expensive in the US, effectively creating homelessness traps.
As for following in the footsteps of Houston, it's not nearly as feasible for these places. They have up to 10x the homeless populations and 2-3x the housing costs. Compare providing 5,000 units in Houston vs providing 70,000 in Los Angeles.
We should absolutely look to provide more subsidized housing to the needy, but it's clear we aren't aren't able to do it in the most in demand real estate markets in country.
EDIT: numbers