It's whole apartment rentals that are illegal. Where is grandma living while she is renting out her rent control apartment, that she pays $900/month for, on AirBnB for $300 a night? Maybe in her second, supposedly not primary, home in Florida?
In any event, I don't suggest they evict hosts. What I suggest is they go after AirBnB for continuing to accept blatantly illegal listings, like this one for example: https://www.airbnb.com/rooms/16148374
While section Section 230 of the CDA is an issue, the fact that AirBnB is taking money from the rental turns this into more than just a third party publisher of information. If Cy Vance wasn't too busy taking campaign donations to look the other way for powerful people, I'm sure he could direct his office to come up with something. Or Berman in SDNY could.
Well, you have a huge city with expensive hotels (the most expensive hotels in Vegas are sometimes cheaper than really average hotels in New York). So, the number of people willing to risk it to make a quick buck is not going to be small.
In addition, there is somewhat of a PR problem for NYC. Kicking people out of their apartments, especially in winter, makes for great outrage news stories--especially if you happen to evict some 82-year-old grandma in rent control who is using AirBnB to pay for her meds.
Better to simply notify the landlords, like San Francisco does, who are then incentivized to evict the scofflaws.