What would the police do about it, arrest the homeless person? Would the local criminal justice system have the capacity to charge and convict them if the cops did so? Many of the cities where visible homelessness is a problem also have shortages of cops that cause them to triage what sorts of incidents they send an officer to respond to?
I probably would not have called the police after this person if this happened to me, because I expect they would do nothing about it.
Where do you live?
In the U.S. police will show up, investigate, and absolutely arrest someone who made a loud, direct, threat to murder another human being in public.