As far as going somewhere else, the problem is accessibility of resources for the unhoused. Many municipalities don't like the idea of random people going to their town and using the benefits from that town, you have to have lived in that town for many years and ostensibly contributed taxes while you were able to work. So if you were previously housed in LA/NYC, your best bet to getting services is to stay there because having been housed there previously gets you moved up on the list for housing.
