It's possible I've misread the host pool, but 80%+ of the places I've stayed at have not been professionally managed apartments, but rather people subletting a room or their entire place when traveling, and doing some quick reverse image searching shows that these places are not available on any alternative sites, for them an exclusivity arrangement doesn't even matter because they were not going to rent elsewhere.
If people sidestepping AirBnB became common, it would be a pretty easy decision for AirBnB to enforce exclusivity and just say goodbye to everyone else, because people showrooming on AirBnB is actively harmful to them vs not having that inventory.
If you're in an area with 100s of hits in a square mile, you have no real leverage here by definition.
Exclusivity contracts? What's my incentive as a host there? Is AirBnB going to give me more of a cut?
Is AirBnb going to make "exclusivity" actually mean something, and not give me 100s of hits in a square mile or two, so that my listing doesn't appear on page 10 of the results?