So your solution for homelessness is ... shooting random homeless people? Even "self defense" carries with it a test for proportional response.
Defending yourself from a person who hits you in the head with a hard object is reasonable (at least in the rest of the world outside of California), shooting too.
That's not even remotely what the parent said. Random homeless people != Homeless person assaulting you.
Wouldn't it be easier to just help the homeless person to not be desperate, offer treatment, and home with TV..
(A room with a TV is a cheap way to prevent crime)