I think the bigger issue is if the externalities imposed by normal usage are so high that, when properly internalized, AirBNB no longer presents a compelling value proposition in the majority of cases. This is certainly possible.
From AirBNB's perspective, perhaps they just fight the internalization as hard as possible. There are businesses with much costlier externalities, such as energy companies, that are actually subsidized and not taxed. In the AirBNB case, however, they may have a tougher fight as the harm, while lower in aggregate, is also less diffuse.