There are laws in New York City that say (with good reason) that you can't just turn your home into a hotel. New York is simply enforcing the law.
If Airbnb really has the public support they claim then it should be easy to change the law. The reality is a lot (likely vast majority) of New Yorkers really don't want the status quo to change. The politicians know this and hence why they took this path.
Maybe this is good law in New York City because its so dense and everyone is stepping on one another, but its not good law for the entire, gigantic state of New York.
My cousin does cleaning and management of vacation rentals in the Catskills, in parts of New York that used to be vibrant but are now extremely economically depressed and taxed exorbitantly.
Forbid vacation rentals that violate noise ordinances, don't cast generalization blankets and act out of prejudice.
If Airbnb really has the public support they claim then it should be easy to change the law. The reality is a lot (likely vast majority) of New Yorkers really don't want the status quo to change. The politicians know this and hence why they took this path.