Considering that the landlord sees nothing from the AirBnb'ing, and they have some legal ability to classify their building as "no AirBnb", what sane landlord wouldn't do it? This goes doubly if rents in non-AirBnb buildings are, as you suggested, higher.

Landlords won't allow AirBnB, they'll be AirBnB. They'll disallow it for long term tenants, yet always have every vacant unit listed on the site. If they can book it for a week, they'll make what you currently pay for the month's rent. Depending on how well you're located, there's going to be some pressure on your rent.