The profit doesn't come solely from pushing away externalities. It also profits by tapping into more transient supply of accommodation by home-owners. That is,

The profit doesn't come solely from pushing away externalities. It also profits by tapping into more transient supply of accommodation by home-owners. That is, people who happen to own a home but aren't living there at the moment, or who are willing to share the space. This doesn't apply to people who buy houses with the intent to airbnb them, they are purely about avoiding hotel regulations.