NYC has 10% of the entire USA's homeless population. Significantly more if you count the (probably large) percentage of the 635,000 or so in public housing who will almost never be able to afford even rent-stabilized apartments, and it is estimated that another 50% of that number live in that public housing off-lease.
About 10% - 15% of NYC homeless are formally listed as last address "outside NYC". But that likely vastly undercounts, because people might have had a relative or friend where they crashed for a few months, weeks... just long enough to get addresses for a few ids/bills to be switched over.
There simply isn't any more cheap land with good public transit infrastructure for new low cost housing, a huge low-skilled (often illegal) immigrant population, and no one wants to face reality.
If it's anything like the mentally ill streaming into SF in some parts of recent history, they are shipped there by outside localities (lots of that's happened with one-way bus tickets for homeless in various directions on the west coast, too, aside from Nevada shipping mentally ill to SF.)
> But let's be charitable: we can fund a one-way ticket back, first class, to their state of residence at a vastly cheaper cost than for housing them on expensive land they will never be productive enough to work their way out of
Which is a good way to collapse wages and overwhelm infrastructure, both physical and social, in the place they get shipped (which won't be their “state of residence” in most cases, since that's where they are now), but I don't see how that solves any problem.