I agree with you to some extend.

What I do not agree about is the implicit assumption that if AIRBNB is banned then every house that was used for short-term rental would become available on the long-term rental market.

The main advantage of the short-term rental (obvious higher profits aside) is the fact that the owner is sure to be able to get back the house if/when he need it. So many owners saw the possibility to use an house with AirBnB (or other similar ways) a lot more attractive than keeping it empty (paying the taxes on it) and much less risky than having a long-term rental where the tenants could be turn out to be a bad one.