The neat property of this business model is that it's actually viral: the way to avoid getting screwed by AirBnBers next door is to rent your place out on AirBnB too, and then go stay in somebody else's AirBnB.
It can be interesting to try and consider the endgame of various startups' business models, basically what the world would look like if the economic inefficiency they exploit is arbitraged away entirely. YCombinator is a world where everyone is an entrepreneur, but the returns to entrepreneurship aren't much better than having a regular job, and everybody works much harder. Google is "information wants to be free", where everybody has full access to information and the market price of that is zero. Napster was that nobody would produce art or music; Facebook is that all socializing occurs online; Uber/DoorDash/PostMates and other sharing economy startups create a caste society where those without technical skills serve those who do. AirBnB's endgame is the destruction of the concept of residency. If they succeed in their mission and arbitrage away all inefficiencies in the housing market, they effectively institutionalize the digital nomad lifestyle, where everybody can live and work anywhere in the globe, and yet never has a permanent home.
I'll let other people judge whether that's a good or bad thing. To me, most social institutions are pretty arbitrary anyway, and I have confidence I could adapt to whatever world comes next. I'll say that they're riding a really powerful trend that's independent of any one corporation or individual: the Internet has made nearly all markets global, and so the idea of being tied to a particular place is becoming increasingly quaint for many people.