Economics (and math) is only useful to life insofar as its axioms model reality well.
If you put a value on human life and model flux across borders, the metrics look different than purely $ spent for # of homeless present.
See Also: where most public school funding goes.
Chronically homeless folks make up only ~25% of the homeless population and of them less than half have mental illness or addiction issues. So, most chronically homeless people can be helped with housing and other measures.
My point is just that the crazy yelling homeless guy you see on the street in SF is a minority when it comes to the homeless population. You are just much more likely to see him because he is yelling on the street in SF. However, for every crazy homeless guy yelling, there are >5 people living in their cars who just need some temporary help to get back on their feet.
You aren't suggesting that providing housing to the homeless will lead to more violence than when the homeless live on the streets, are you?
I suspect that this is because the 'place to stay' usually comes with various strings attached. I doubt there are many homeless people who would choose to sleep under a bridge rather than in a bed (though not doubt there are a minority who would).
So the options are to cut social programs, leave them as they are now, or expand them. Which option would you guess has the best chances of helping more people?