Many (most?) of the homeless you see around you are your community. They don't need to be invited into the city because it's their home too.
I live in SF and I know homeless people who have lived on the same street corner longer than some of my coworkers have lived in the city (or even the country). Many of the people who experience such misfortunes - even drug addicts who behave poorly - are long-time residents who once helped make the city the place it is. Sure their behave causes issues, and society needs to do something, but implying they don't have a claim to be helped in their own city is unfair.