Rather audaciously, Airbnb DO actually appear to feel that they have ownership over hosts' repeat bookings, and have prohibited hosts from asking or encouraging guests to book outside of Airbnb for any return stays, under penalty of suspension or delisting.
Imagine ordering a lovely dish
from a restaurant you discovered on Uber Eats, and then Uber Eats trying to forbid you from ever going directly to that restaurant when you fancy a meal from there again...
Hilarious.