If that were the case we wouldn't see the chronically homeless all disproportionately clustered around areas where housing costs have exploded, and it's not just because of money spent on services there.
The homeless are always going to flock to where the people with money are.
It does seem counterintuitive, but when your local economy is shit (i.e. panhandling in ghettos), you're going to emigrate somewhere with more opportunity.
>> 70% of people homeless in San Francisco in 2019 reported becoming homeless while living in San Francisco: 22% came from another county within California, and 8% came from another state.
