Also, NY specifically worries that it will change the local housing market. If investors buy up enough local properties and turn them into mini hotels, locals may be priced out of these neighbourhoods and those neighbourhoods will in turn suffer.
Plus there are the complaints from the locals. Having a neighbour rent out their place to tourists a couple of times a year is not a big deal, but if it happens every single week it gets annoying. You never know who is coming and going and they aren't always all that worried about noise, garbage, etc.
And just to clarify, I think the state is right to be concerned about these issues. But at the same time I would hate to lose the ability for someone to put their primary residence on a site like Airbnb a couple of times a year. This helps visitors and the residents without significantly hurting anything else in the equation. Things only start to turn sour when enough people create dedicated Airbnb properties as investments.