SF gets described as 'housing first', but it certainly does not act like it. In SF, we actually have unspent funds from our 2018 "Prop C" ballot initiative which dedicated funding to specific categories, the largest of which was for permanent housing. I.e. there has been money available for 5 years for permanent housing, but the city is not willing to buy available units -- it will only consider developing new projects, which get stuck in planning hell, and have extremely high per-unit costs. The city is not willing to rent vacant market-rate units, even when large numbers are available, including in rent-stabilized buildings, where it could have long-term predictable rents. When rents dropped sharply during the pandemic, we did not put people into empty, cheap apartments. Instead, we payed $5k/month per tent in parking lot safe sleeping sites.
Mayor Breed is also trying to take funds which are set aside for permanent housing and use them for shelter beds and prevention services.
Funding exists to put more people into actual housing basically immediately, but the city instead pursues more shelter beds and ever larger contracts with Urban Alchemy.