And you know what? I'm not sure if they should.
My family has used VRBO ("vacation rental by owner") to rent apartments in Paris, Amsterdam, and Budapest over the last three summers. We loved the experience, and would never even consider going to a hotel in the future, for all of the reasons you can imagine -- we save money, cook our own meals, and feel at "home" in a foreign city. It's a marvelous feeling.
But that marvelous feeling is probably less-than-marvelous for a city's permanent residents. When we stayed in Paris, we were told that short-term rentals there are illegal partly because housing is in short supply, and is thus astronomically expensive. Forbidding short-term rentals, in theory, can increase the pool for annual rentals, thus bringing the cost down. (We were also told that rental law was 100 years old, but was only now going to be enforced. Amusingly, we were also told that the French justice minister lived in our building...)
Plus, I don't know if I would want an apartment in my building to be occupied by new people each week. We have enough trouble with the neighbors we know.
Bottom line, AirBNB is a brilliant idea, and many people clearly love it. But I don't think that they, or we, can expect laws to change immediately to accommodate this new idea. And when the laws do change, we can probably expect them to still impose some restrictions, or even taxes, on the homeowners.