If those are the actual numbers, you're proving GP's point. You can give each of those 14.5k people ~$55-60k instead of giving 8k people $100k and homelessness is still solved.
It's unlikely there's a trivial arbitrage to eliminate homelessness in a city full of engineers.
It’s like history was the first casualty of late stage capitalism and no one knows about the new deal or the war on poverty.