I think your missing a huge one. Taxes, hotels in major city's often send 10+$ a day to the local government. And before people complain about this that money often pays for things like museums and convention centers which is why many people are going to the city in the first place.
So if NYC just made airbnb charge the 5.875% tax, most of their complaints would go away? And by increasing the hotel supply, hotel prices would go down to better match actual long term renting? Then it would create a more liquid housing market enabled by computerized markets? It would still allow casual renting of people's houses that way.
No, their complaints aren't strictly about the missing tax revenue. There are other regulations that would need to be addressed (health, safety, etc...). Hotels are a heavily regulated industry with good reason. Regulations are a protection mechanism to protect the city/neighborhood and the consumer.
I think that there is a clear difference between renting out a room or occasionally renting your entire place, versus keeping a separate apartment strictly for renting out on AirBnB.
Edit: NY get's 10$ on a one room 140$ hotel room stay as it's $2.00 per day per room* + 5.875% of the rent. http://www.nyc.gov/html/dof/html/business/hotel.shtml