Unfortunately, I do believe the extra burden will lead to less construction and I worry that short-term stays will indeed become more expensive because of the lower supply of rooms.
In many parts of the city hotels have already outpaced other non-residential development. These regulations, on top of supporting union workers, just ensure that hotels don't take over too much of certain parts of the city. The biggest issue with AirBNB is that you have unregulated conversion of residential property into short term hotels, which impacts long term residents living in the city. A hotel shortage mostly impacts tourism, which is already booming in the city and is a less critical issue for NYC residents.
Unfortunately, I do believe the extra burden will lead to less construction and I worry that short-term stays will indeed become more expensive because of the lower supply of rooms.