I don't really know how you start with the premise that travel isn't a race to the bottom. If you think customers have zero loyalty toward hired cars then you haven't dealt with travel customers. Business notwithstanding, travel a typically a large expense in both money and time. Customers will aggressively shop for the lowest prices and Airbnb is just one category of alternative for customers looking to travel -- BnBAir isn't even close to their biggest threat, although the rise of meta-travel agencies does suggest that it might be in the future.
Also, hotels list on many different travel sites. Why wouldn't AirBnB hosts? It's basically zero cost for potentially more customers. Hell hosts would probably be willing to list on 10+ individual sites for all it costs them.