You don't need airbnb to rent a place; you just need a web page with e-mail and phone number.
It's about the visibility.
I've stayed in places whereby I phoned the owner to make a reservation and that was that. It is actually a "thing".
There are sites that aggregate listings of places like that without serving as a go between. It's not like the operators of the B&B just put up a page and rely on nothing but search engine indexing.