AirBNB is illegal not only due to short term hotel law, but also due to sublease law in NYC. You CANNOT sublet an apartment for more than it is worth in New York. I've met and heard of more than a few people who rent apartments and use AirBNB as a primary source of (as OP points out, untaxed) income. I'm surprised NYC landlords aren't more up in arms about this.
I don't agree with making it illegal outright, but I actually am kind of in favor of regulating and taxing this better, for the issues the OP talks about as well as the sublease issues.
Edit: After thinking about this a little more I realize the OP goes 90% of the way but doesn't quite cross the finish line with the argument. AirBNB IS the regulatory institution, and is doing a better job than the govt. My sublease point still stands.