I don't think this can work. A person is either legally entitled to AirBnb their place, or they aren't. If the choice is given to the landlord to create "no AirBnb" buildings, you can bet your ass that just about
every single building will be declared no-AirBnb.
Short term rentals present risk to landlord - damage of common property, excessive resource consumption (electric, hot water, gas, etc, that may not be paid directly by lease-holder). How high this risk is is a topic of hot debate, but it's certainly a non-zero number.
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.
This leads naturally to the thought that we can incentivize landlords to allow AirBnbs (read: kickbacks) - at which point AirBnb starts looking an awwwwful lot like traditional hotels, or worse, the slum-tels of old.
Side note: giant companies like AirBnb keep using the word "sharing economy", which I find highly disingenuous. This isn't early-stage eBay, where you list things you don't need. It also isn't Craigslist. The vast majority of places on AirBnb aren't "I'll be out of town and I'd like to make some money on my apartment", the vast majority of AirBnbs are dedicated operations. A far cry from the "peer to peer" "efficient use of excess resources" that Lyft, Sidecar, AirBnb, et al, like to talk about.
We hate it when politicians use doublespeak, why do we so readily allow it when it's being done by a company that's on our good side?