1 billion dollars / 8500[1] homeless people = 117 thousand dollars. The median household income in SF is 119 thousand[2]. I get that you wouldn't want to just pay them a salary because of second-order effects, but that kind of spend without even getting them sheltered strongly suggests resources are not being allocated well.
If you gave them $117K a year they would be dead within a month ODing on the mass quantities of drugs they can now afford.
Money is not the issue with homelessness, and until people get that out of their heads the problem will not be solved.
[1] https://www.sfgov.org/scorecards/safety-net/homeless-populat...
[2] https://smartasset.com/retirement/average-salary-in-san-fran...