If the problem is a tiny studio costing twice as much as the median US house, the only fix is the eventual application of the laws of Supply and Demand. Any other solution is either SO tempting to game that you can guarantee it will happen (ref: Rent-controlled apartments, this program) or SO expensive (to somebody… developers, taxpayers, HUD) that it’d never get off the ground.
You don’t have a right to live in New York. This country is a big place, and there are very few middle (much less lower) — class jobs that require residence IN NYC. If you are willing to relocate to the farther reaches of Metro North, or PATH, you get a lot of options, even if they aren’t as hip or desirable. Or, one of the bazillion thriving, vibrant, mid-size cities this country has in abundance.