Previously, vehicle dwelling was prohibited by law everywhere in Los Angeles. A court case forced the city to open up non-residential areas to vehicular living, please read about this via this link. You can see the map of streets where vehicle dwelling is allowed with this link. A street is designated as a green zone because the adjacent properties are zoned as commercial or industrial lots, not because they have been chosen as a good location for vehicle dwelling. Since the development of residential buildings in commercial and industrial areas is happening to help address the housing crisis, I am pushing to have the next iteration of this parking map take into account such development, rather than merely extant zoning alone. The overwhelming majority of our community is residential and these vehicle dwelling maps were designed to prohibit vehicle dwelling in our residential neighborhoods. You will also see this reflected on the map where most streets are red or yellow, meaning vehicle dwelling is either prohibited or restricted by parking regulations that are applied to all vehicles.
Now, it is possible to place parking restrictions on a green zone street, however, this will need to be supported by crime statistics provided by the LAPD. If enough crimes are reported to the LAPD then a case can be made to place parking restrictions for the sake of public safety. It is not legal to base parking restrictions on homelessness, so it is important never to even attempt to justify such a restriction on such grounds. Such a restriction would get overturned by the courts.